Finite Group Databasebeta

← Group #13168579

Character table — Group #13168579

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order1222333666666666333466666666644443666121212121212121212121212124444121212121212121212121212224412121212121212121212121212121212121224446612121212444461212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-111-1-1111111-1-1-1-11-111-1111-1-111-1-11111-111-1-1-111-1-1-1-1-1-1-11-1
χ31111111111111111111111111111111-1-111111111111111111111-1111111-1-111-1-111-1-1111-11-111111111-1-1-1-11-1-1-111-1-1-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111-1-111111111111111111-1-11-1-1-111-1-1-1-111-1-1-1-1111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ511111111111111111111111111111-1-1111111111111111111111-1111-1-11111-1-111-1-111-11-1111-1-111-1-1111111-1-1-11-1-1-1-111-1-1-1-1-1-11
χ611111111111111111111111111111-1-11111111111111111111-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-111111-1-1
χ711111111111111111111111111111-1-1-1-11111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-1-1-1-111-1-1-111-1-11111-11-1
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-11
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-111-11-1-1-1-1-1-11111-1-111-1-11-11-1-1-11111-1-1111-1-1
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111-1-11111-1-1-1111-1-1-1-11111-1-111-11-1-111-1-111-1-111-11-1
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-1-1-1-1-1-11-11-11-1-11111-1-1-1-11111-11-1-1-1-1-1-111-1-1111
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-1-1-11-11-11-111-1-1-1-11111-1-111-11-1-1-1-1-1-1-1-111111
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1111111111-1-1-11111-1-1-1-111-1-1-11-1-111-1-11111-1-1-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1-1-1111-1111111-1-1-1-111-1-1111-11-1-1-1111111-1-11-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-11
χ17222222-12-1-1-1222222-1-122-1-12-1-1-1-122200-1-1-1-1-12222-1-1-1-1-1-1-1-1222022-1-1-1-10022002200-1-12020-1-1-1-1-1-1-1-100002000-1-100000000-100
χ18222222-12-1-1-1222222-1-122-1-12-1-1-1-122200-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-220-2-2-1-111002200-2-200-1120-20-1-111-1-1110000-20001100000000100
χ19222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-200-1-1-1-1-12222-1-1-1-1-1-1-1-122-202211-1-100-2-200-2-2001-1-202011-1-111-1-10000-20001100000000100
χ20222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-200-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-2-2111100-2-200220011-20-201111111100002000-1-100000000-100
χ21222222-12-1-1-1222222-1-1-22-1-12-1-1-1-122200-1-1-1-11-2-2-2-2111111112-2-20-2-2-1-1-1-1002200220011-20201111-1-1-1-10000-2000-1-100000000100
χ22222222-12-1-1-1222222-1-1-22-1-12-1-1-1-122200-1-1-1-11-2-2-2-211111111-22-2022-1-111002200-2-2001-1-20-2011-1-1-1-111000020001100000000-100
χ23222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-200-1-1-1-11-2-2-2-2111111112-220-2-211-1-100-2-200-2-200-112020-1-11111-1-1000020001100000000-100
χ24222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-200-1-1-1-11-2-2-2-211111111-222022111100-2-2002200-1-120-20-1-1-1-111110000-2000-1-100000000100
χ2522222-122222-1-12-12-12-12-12-1-12-12-1-12222-1-1-1-122-1-1-122-1-1-1-1-1-10022002200-1-1-1-122000020-1-102-1-100-1-100-1-1-1-1022000-1-10000000-10
χ2622222-122222-1-12-12-12-12-12-1-12-12-1-122-2-2-1-1-1-122-1-1-122-1-1-1-1-1-1002-200220011-1-1-2-2000020-110-2-1-100-1-10011110-2-200011000000010
χ2722222-122222-1-12-12-12-12-12-1-12-12-1-1-2-222-1-1-1-122-1-1-122-1-1-1-1-1-100-2200-2-200-1-111220000-201-10211001100-1-1-1-10-2-200011000000010
χ2822222-122222-1-12-12-12-12-12-1-12-12-1-1-2-2-2-2-1-1-1-122-1-1-122-1-1-1-1-1-100-2-200-2-2001111-2-20000-20110-2110011001111022000-1-10000000-10
χ2922222-122222-1-12-12-12-1-2-12-1-12-12-1-12222-1-1-1-1-2-2111-2-211111100-2-2002200-1-1-1-1220000-20110-21100-1-100-1-1110-22000-1-1000000010
χ3022222-122222-1-12-12-12-1-2-12-1-12-12-1-122-2-2-1-1-1-1-2-2111-2-211111100-2200220011-1-1-2-20000-201-1021100-1-10011-1-102-2000110000000-10
χ3122222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2-2111-2-2111111002-200-2-200-1-11122000020-110-2-1-1001100-1-11102-2000110000000-10
χ3222222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2-2111-2-2111111002200-2-2001111-2-2000020-1-102-1-100110011-1-10-22000-1-1000000010
χ332222-122-122222-12-1-1-122-1-12-1-12-12-10022-1-1-1-12-12-1-1-1-122-1-1-1-12202-1-100222200-1-100220202-1-100-1-100-1-1-1-1-1-100020000-1-1000000-1
χ342222-122-122222-12-1-1-122-1-12-1-12-12-10022-1-1-1-12-12-1-1-1-122-1-1-1-1-2-2021100-2-22200-1-100-2-20-2021-100110011-1-1-1-1000-20000110000001
χ352222-122-122222-12-1-1-122-1-12-1-12-12-100-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1220-2-1-10022-2-2001100-2-2020-2-1100-1-100-1-11111000-20000110000001
χ362222-122-122222-12-1-1-122-1-12-1-12-12-100-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-2-20-21100-2-2-2-2001100220-20-21100110011111100020000-1-1000000-1
χ372222-122-122222-12-1-1-12-2-1-12-1-12-12-10022-1-1-1-1-21-21111-2-211112-20-21100222200-1-100-2-20-20-2-11001100-1-1-1-1110002000011000000-1
χ382222-122-122222-12-1-1-12-2-1-12-1-12-12-10022-1-1-1-1-21-21111-2-21111-220-2-1-100-2-22200-1-10022020-21100-1-10011-1-111000-20000-1-10000001
χ392222-122-122222-12-1-1-12-2-1-12-1-12-12-100-2-2-1-1-1-1-21-21111-2-211112-202110022-2-2001100220-202-1-1001100-1-111-1-1000-20000-1-10000001
χ402222-122-122222-12-1-1-12-2-1-12-1-12-12-100-2-2-1-1-1-1-21-21111-2-21111-2202-1-100-2-2-2-2001100-2-202021-100-1-1001111-1-10002000011000000-1
χ4122-2-2222-2-2-22-2-222-22220-2-2-22-2-222-2002i−2i2-2-22000000000000000000000002i−2i002i−2i2-200000000000000002i−2i0000002-200002i−2i00000
χ4222-2-2222-2-2-22-2-222-22220-2-2-22-2-222-2002i−2i2-2-22000000000000000000000002i−2i002i−2i-2200000000000000002i−2i000000-220000−2i2i00000
χ4322-2-2222-2-2-22-2-222-22220-2-2-22-2-222-200−2i2i2-2-2200000000000000000000000−2i2i00−2i2i2-20000000000000000−2i2i0000002-20000−2i2i00000
χ4422-2-2222-2-2-22-2-222-22220-2-2-22-2-222-200−2i2i2-2-2200000000000000000000000−2i2i00−2i2i-220000000000000000−2i2i000000-2200002i−2i00000
χ452-2-22222-22-2-22-2-2-222220-22-2-2-22-2-222i−2i0022-2-200000000000000000002i−2i00002i−2i00002i−2i00000000002i−2i000000000000002i−2i002-2000
χ462-2-22222-22-2-22-2-2-222220-22-2-2-22-2-222i−2i0022-2-200000000000000000002i−2i00002i−2i0000−2i2i00000000002i−2i00000000000000−2i2i00-22000
χ472-2-22222-22-2-22-2-2-222220-22-2-2-22-2-22−2i2i0022-2-20000000000000000000−2i2i0000−2i2i00002i−2i0000000000−2i2i000000000000002i−2i00-22000
χ482-2-22222-22-2-22-2-2-222220-22-2-2-22-2-22−2i2i0022-2-20000000000000000000−2i2i0000−2i2i0000−2i2i0000000000−2i2i00000000000000−2i2i002-2000
χ4944444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-244001111-24-2-2-2-2-2111111004000-2-20000-2-2000000-20-200011001100000000000000000000000
χ5044444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-2-4-4001111-24-2-2-2-2-211111100-400022000022000000202000-1-100-1-100000000000000000000000
χ5144444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-2440011112-422222-1-1-1-1-1-100-4000-2-20000-2-2000000202000-1-1001100000000000000000000000
χ5244444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-2-4-40011112-422222-1-1-1-1-1-100400022000022000000-20-20001100-1-100000000000000000000000
χ534444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-200001111-2-24-2-211-2-211114400-2-200-2-200000000000-200-2000110011000000000000000000000
χ544444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-200001111-2-24-2-211-2-21111-4-400220022000000000002002000-1-100-1-1000000000000000000000
χ554444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-20000111122-422-1-122-1-1-1-14-4002200-2-200000000000200-2000-1-10011000000000000000000000
χ564444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-20000111122-422-1-122-1-1-1-1-4400-2-2002200000000000-20020001100-1-1000000000000000000000
χ574444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-21004411114-2-211-2-2-2-211110004000000-2-200-2-20000000-20-200000000111100000000000000000
χ584444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-2100-4-411114-2-211-2-2-2-21111000-4000000220022000000020200000000-1-1-1-100000000000000000
χ594444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-2100441111-422-1-12222-1-1-1-1000-4000000-2-200-2-200000002020000000011-1-100000000000000000
χ604444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-2100-4-41111-422-1-12222-1-1-1-100040000002200220000000-20-200000000-1-11100000000000000000
χ6144-4-444-2-422-2-4-444-44-2-20-422422-2-2-40000-222-2000000000000000000000000000004-4000000000000000000000000-2200000000000
χ6244-4-444-2-422-2-4-444-44-2-20-422422-2-2-40000-222-200000000000000000000000000000-440000000000000000000000002-200000000000
χ6344-4-44-24-4-4-44224-2-4-24-202-42-2-424-22004i−4i-222-200000000000000000000000−2i2i004i−4i000000000000000000−2i2i0000000000000000000
χ6444-4-44-24-4-4-44224-2-4-24-202-42-2-424-2200−4i4i-222-2000000000000000000000002i−2i00−4i4i0000000000000000002i−2i0000000000000000000
χ6544-4-4-2442-4-44-4-4-242-2-24022-4-22-4-242004i−4i-222-2000000000000000000000004i−4i00−2i2i000000000000000000−2i2i0000000000000000000
χ6644-4-4-2442-4-44-4-4-242-2-24022-4-22-4-24200−4i4i-222-200000000000000000000000−4i4i002i−2i0000000000000000002i−2i0000000000000000000
χ6744-4-4-2-242-4-4422-2-221-2-20-122122-2-2-1004i−4i1-1-110003-3000033-3-30000000000−2i2i00−2i2i000000000000000000i−i3i−3i00000000000000000
χ6844-4-4-2-242-4-4422-2-221-2-20-122122-2-2-1004i−4i1-1-11000-330000-3-3330000000000−2i2i00−2i2i000000000000000000i−i−3i3i00000000000000000
χ6944-4-4-2-242-4-4422-2-221-2-20-122122-2-2-100−4i4i1-1-110003-3000033-3-300000000002i−2i002i−2i000000000000000000−ii−3i3i00000000000000000
χ7044-4-4-2-242-4-4422-2-221-2-20-122122-2-2-100−4i4i1-1-11000-330000-3-33300000000002i−2i002i−2i000000000000000000−ii3i−3i00000000000000000
χ714-44-44444-44-4-44-4-4-444404-44-44-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ724-44-444-242-22-44-4-4-44-2-2042-2-4-2222-40000-22-2200000000000000000000023−23000000000000000000000023−23000000000000000000000
χ734-44-444-242-22-44-4-4-44-2-2042-2-4-2222-40000-22-22000000000000000000000−23230000000000000000000000−2323000000000000000000000
χ744-44-44-244-44-42-2-42-4-24-20-2-4-2242-4220000-22-22000000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ754-44-44-244-44-42-2-42-4-24-20-2-4-2242-4220000-22-220000000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ764-44-4-244-2-44-4-442-42-2-240-2242-2-42-420000-22-2200000000000000000−2i32i30000000000000000000000−2i32i30000000000000000000000000
χ774-44-4-244-2-44-4-442-42-2-240-2242-2-42-420000-22-22000000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000000000
χ784-44-4-24-2-22-22-442-42-21-20-2-1-2212-12200001-11-1000003i−3i003i−3i3i−3i0000−2i32i30023−23000000000000000000i3−i300−33000000000000000000000
χ794-44-4-24-2-22-22-442-42-21-20-2-1-2212-12200001-11-1000003i−3i003i−3i3i−3i00002i3−2i300−2323000000000000000000−i3i3003−3000000000000000000000
χ804-44-4-24-2-22-22-442-42-21-20-2-1-2212-12200001-11-100000−3i3i00−3i3i−3i3i0000−2i32i300−2323000000000000000000i3−i3003−3000000000000000000000
χ814-44-4-24-2-22-22-442-42-21-20-2-1-2212-12200001-11-100000−3i3i00−3i3i−3i3i00002i3−2i30023−23000000000000000000−i3i300−33000000000000000000000
χ824-4-4444-2-4-2224-4-4-444-2-20-4-22-42-22244i−4i00-2-2220000000000000000000−2i2i00004i−4i0000000000000000−2i2i00000000000000000000000
χ834-4-4444-2-4-2224-4-4-444-2-20-4-22-42-2224−4i4i00-2-22200000000000000000002i−2i0000−4i4i00000000000000002i−2i00000000000000000000000
χ844-4-444-24-44-4-4-22-424-24-202422-4-2-42-24i−4i00-2-22200000000000000000004i−4i0000−2i2i0000000000000000−2i2i00000000000000000000000
χ854-4-444-24-44-4-4-22-424-24-202422-4-2-42-2−4i4i00-2-2220000000000000000000−4i4i00002i−2i00000000000000002i−2i00000000000000000000000
χ864-4-444-2-2-4-222-22-424-2-2102-2-12212-1-24i−4i0011-1-100000003i−3i3i−3i−3i3i000000−2i2i0000−2i2i0000000000003-300i−i00000000000000000000000
χ874-4-444-2-2-4-222-22-424-2-2102-2-12212-1-24i−4i0011-1-10000000−3i3i−3i3i3i−3i000000−2i2i0000−2i2i000000000000-3300i−i00000000000000000000000
χ884-4-444-2-2-4-222-22-424-2-2102-2-12212-1-2−4i4i0011-1-100000003i−3i3i−3i−3i3i0000002i−2i00002i−2i000000000000-3300−ii00000000000000000000000
χ894-4-444-2-2-4-222-22-424-2-2102-2-12212-1-2−4i4i0011-1-10000000−3i3i−3i3i3i−3i0000002i−2i00002i−2i0000000000003-300−ii00000000000000000000000
χ904-4-44-24424-4-44-42-4-2-2-2402-2-42242-4-20000-2-22200000000000000000000000000000004i−4i00000000000000000000000000−2i2i0000000
χ914-4-44-24424-4-44-42-4-2-2-2402-2-42242-4-20000-2-2220000000000000000000000000000000−4i4i000000000000000000000000002i−2i0000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-422282222222220000-1-1-1-1-4-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222220000-1-1-1-1444-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9488-8-88-4-4-844-4448-4-8-4-42044-2-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-48-4444-4-8-8-484-42-404-24-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4444-444-4-442220-2-2-22-2-222-20000-111-10006-60000-3-3330000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4444-444-4-442220-2-2-22-2-222-20000-111-1000-66000033-3-30000000000000000000000000000000000000000000000000000000
χ988-88-88-4-484-444-4-84-8-4-420-4424-4-24-2400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-48-4-88-84-44442-4-4024-4-2-4444-200002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4-44-444-444422202-22-22-2-2-2-20000-11-11000006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-44-444-444422202-22-22-2-2-2-20000-11-1100000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-44-4448-84-8-4-42-404244-2-4-24-4000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4848-8-8-4444-42-4-40-2-44-24-4442000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-444-4444-42220-22-2-2-22-2-220000-1-11100000006i−6i−3i3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-444-4444-42220-22-2-2-22-2-220000-1-1110000000−6i6i3i−3i−3i3i0000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).