Finite Group Databasebeta

← Group #13168069

Character table — Group #13168069

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666633346666666662236661212121212121212121212121222444666666661212121244666666661212121212121212121222444661212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111111111-1-1-1-1-1-1111111111-11-111-1-1-1-11-1-1-1111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-1-111111-1-111-1-11111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-111-1-111-1-1-1-1-1-111-1-111-1-1-1-11-11-111-1-1-1-1-11-1-1-1-1-111-1-1111-1-11
χ511111111111111111111111111111-1-111111111111111111111-11-1-111-1-11111111111-1-11111-11-11-1-11111-11-1-1-1-1-111-1-1-1-11-1-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-1-1111-1-1-1-111-11-11
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-111-1-1-111111-1-1-11-1-1-1-1-1-111-111-11-1-1-1-111-1-111-11
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-111-1-111-111111-1-1-1-1-11-1-111-1-1-1-1-111-1-111-1-111-111-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111-111-1-111-11-1-1-1-1-1-1111-11-1-111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111-1-1-1-11-111-1-111-1-1-11-1-111-1-111-11-111-1-1-1-1-1-11-111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-1-1-111-1-1-11-1-111-1-1111-111-1-11111-11-111-1-1-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-111-1-111-11-1-111-1-11-1111111-1-11-11-1-1111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111111-1-1-1-1-111111-111-1-111-1-1-111-1-111-1-1-1-1-1111
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1111-1111111-1-1-111-11-1-1-1-1111111-1-1
χ17222222-122-1-122-1222-1-122-1-1-1-1-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-1220202222-1-1-1-10000002-1-1-1-1-1-1-1-1020-1-1000020002-1-10000000-100
χ18222222-122-1-122-1222-1-122-1-1-1-1-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-2-202022-2-2-1-111000000-21-1-11111-1020-1-10000-2000-2110000000100
χ19222222-122-1-122-1222-1-122-1-1-1-1-12-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1220-20-2-22211-1-10000002-111-1-1-1-110-20110000-2000-2110000000100
χ20222222-122-1-122-1222-1-122-1-1-1-1-12-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20-20-2-2-2-21111000000-2111111110-2011000020002-1-10000000-100
χ21222222-122-1-122-1222-1-1-22-1-1-1-1-12-1222-1-1-1-11-2-21111-2-211112-20-202222-1-111000000-2-1-1-1-1-11110-20110000-20002110000000-100
χ22222222-122-1-122-1222-1-1-22-1-1-1-1-12-1222-1-1-1-11-2-21111-2-21111-220-2022-2-2-1-1-1-100000021-1-111-1-110-201100002000-2-1-10000000100
χ23222222-122-1-122-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-2-21111-2-211112-2020-2-2221111000000-2-111-1-111-1020-1-100002000-2-1-10000000100
χ24222222-122-1-122-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-2-21111-2-21111-22020-2-2-2-211-1-1000000211111-1-1-1020-1-10000-20002110000000-100
χ2522222-122-122-122-12-12-12-12-1-12-1-12-100-1-1-1-12-1222-1-1-1-1-1-1-1-12220200-1-10022-1-12222-1200-1-1-1-10-10200-1-1-1-10200000-1-10000-1000
χ2622222-122-122-122-12-12-12-12-1-12-1-12-100-1-1-1-12-1222-1-1-1-1-1-1-1-122-20-200-1-1002211-2-2-2-2-1200-1-1-1-1010-20011110-2000001100001000
χ2722222-122-122-122-12-12-12-12-1-12-1-12-100-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-2202001100-2-2-1-122-2-21-20011110-10200-1-1-1-10-2000001100001000
χ2822222-122-122-122-12-12-12-12-1-12-1-12-100-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-2-20-2001100-2-211-2-2221-2001111010-20011110200000-1-10000-1000
χ2922222-122-122-122-12-12-1-2-12-1-12-1-12-100-1-1-1-1-21-2-2-2111111112-220-200-1-100-2-21122-2-21200-1-1110-10-20011-1-10200000110000-1000
χ3022222-122-122-122-12-12-1-2-12-1-12-1-12-100-1-1-1-1-21-2-2-2111111112-2-20200-1-100-2-2-1-1-2-2221200-1-111010200-1-1110-200000-1-100001000
χ3122222-122-122-122-12-12-1-2-12-1-12-1-12-100-1-1-1-1-21-2-2-211111111-2220-200110022112222-1-20011-1-10-10-20011-1-10-200000-1-100001000
χ3222222-122-122-122-12-12-1-2-12-1-12-1-12-100-1-1-1-1-21-2-2-211111111-22-20200110022-1-1-2-2-2-2-1-20011-1-1010200-1-1110200000110000-1000
χ332222-122-12222-122-1-1-122-1-122-12-1-1-122-1-1-1-122-1-1-122-1-1-1-1-1-100222-1-100220022-1-10000-1-1000022-1-1-1-1-1-1-1-1002200000-1-10000-10
χ342222-122-12222-122-1-1-122-1-122-12-1-1-122-1-1-1-122-1-1-122-1-1-1-1-1-100-22-2-1-1002200-2-2110000-1-100002-2-11-1-1111100-2-20000011000010
χ352222-122-12222-122-1-1-122-1-122-12-1-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-1002-221100-2-20022-1-10000110000-221-111-1-1-1-100-2-20000011000010
χ362222-122-12222-122-1-1-122-1-122-12-1-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-100-2-2-21100-2-200-2-2110000110000-2-211111111002200000-1-10000-10
χ372222-122-12222-122-1-1-12-2-1-122-12-1-1-122-1-1-1-1-2-2111-2-2111111002-2-2-1-1002200-2-2-1-10000-1-10000-22111111-1-1002-200000-1-1000010
χ382222-122-12222-122-1-1-12-2-1-122-12-1-1-122-1-1-1-1-2-2111-2-211111100-2-22-1-100220022110000-1-10000-2-21-111-1-11100-2200000110000-10
χ392222-122-12222-122-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-2-2111-2-21111110022-21100-2-200-2-2-1-1000011000022-11-1-111-1-100-2200000110000-10
χ402222-122-12222-122-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-2-2111-2-211111100-2221100-2-200221100001100002-2-1-1-1-1-1-111002-200000-1-1000010
χ412-22-222222-2-2-2-22-2-22220222-2-2-2-2-2-22-222-2-20000000000000000002-2002-20000002i−2i002-20000000000000000000002i−2i002i−2i0000
χ422-22-222222-2-2-2-22-2-22220222-2-2-2-2-2-22-222-2-20000000000000000002-2002-2000000−2i2i002-2000000000000000000000−2i2i00−2i2i0000
χ432-22-222222-2-2-2-22-2-22220222-2-2-2-2-2-2-2222-2-2000000000000000000-2200-220000002i−2i00-220000000000000000000002i−2i00−2i2i0000
χ442-22-222222-2-2-2-22-2-22220222-2-2-2-2-2-2-2222-2-2000000000000000000-2200-22000000−2i2i00-22000000000000000000000−2i2i002i−2i0000
χ4544444-2-24-2-2-2-24-2-24-2-214-2-211-21-2-2-2001111-2-24-2-211-2-211114400000-2-200-2-2000000-2-2001111000000000000000000000000000
χ4644444-2-24-2-2-2-24-2-24-2-214-2-211-21-2-2-2001111-2-24-2-211-2-21111-4-4000002200220000002200-1-1-1-1000000000000000000000000000
χ4744444-2-24-2-2-2-24-2-24-2-21-4-2-211-21-2-2-200111122-422-1-122-1-1-1-14-400000-2-200220000002-20011-1-1000000000000000000000000000
χ4844444-2-24-2-2-2-24-2-24-2-21-4-2-211-21-2-2-200111122-422-1-122-1-1-1-1-44000002200-2-2000000-2200-1-111000000000000000000000000000
χ494444-24-2-24-2-24-2-24-2-21-24-21-2-21-2-21-2441111-24-211-2-2-2-2111100040-2-200-2-20000000000110000-20-2011000000000000000000000
χ504444-24-2-24-2-24-2-24-2-21-24-21-2-21-2-21-2-4-41111-24-211-2-2-2-21111000-402200220000000000-1-100002020-1-1000000000000000000000
χ514444-24-2-24-2-24-2-24-2-21-2-4-21-2-21-2-21-24411112-42-1-12222-1-1-1-1000-40-2-200-2-200000000001100002020-1-1000000000000000000000
χ524444-24-2-24-2-24-2-24-2-21-2-4-21-2-21-2-21-2-4-411112-42-1-12222-1-1-1-1000402200220000000000-1-10000-20-2011000000000000000000000
χ534444-2-24-2-244-2-24-2-21-2-241-2-2-2-2-21-210011114-2-2-2-2-2-21111110040400000000-2-2-2-200000000000-20-200111100000000000000000
χ544444-2-24-2-244-2-24-2-21-2-241-2-2-2-2-21-210011114-2-2-2-2-2-211111100-40-40000000022220000000000020200-1-1-1-100000000000000000
χ554444-2-24-2-244-2-24-2-21-2-2-41-2-2-2-2-21-21001111-4222222-1-1-1-1-1-10040-40000000022-2-200000000000-20200-1-11100000000000000000
χ564444-2-24-2-244-2-24-2-21-2-2-41-2-2-2-2-21-21001111-4222222-1-1-1-1-1-100-40400000000-2-2220000000000020-20011-1-100000000000000000
χ5744-4-4444-4-44-44-4-4-444440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-4-224-42-444-2-20-4222-2-2-42400-222-2000000000000000000000000−2i32i3000000000000−2i32i3000000000000000000000000000
χ5944-4-444-2-4-4-224-42-444-2-20-4222-2-2-42400-222-20000000000000000000000002i3−2i30000000000002i3−2i3000000000000000000000000000
χ6044-4-44-24-424-4-2-4-424-24-202-4224-22-4-200-222-200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ6144-4-44-24-424-4-2-4-424-24-202-4224-22-4-200-222-2000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ6244-4-44-2-2-42-22-2-4224-2-21022-1-1-2122-2001-1-11000003-30033-3-30000000−2i32i300−2i32i30000000000i3−i3i3−i3000000000000000000000000000
χ6344-4-44-2-2-42-22-2-4224-2-21022-1-1-2122-2001-1-11000003-30033-3-300000002i3−2i3002i3−2i30000000000−i3i3−i3i3000000000000000000000000000
χ6444-4-44-2-2-42-22-2-4224-2-21022-1-1-2122-2001-1-1100000-3300-3-3330000000−2i32i3002i3−2i30000000000i3−i3−i3i3000000000000000000000000000
χ6544-4-44-2-2-42-22-2-4224-2-21022-1-1-2122-2001-1-1100000-3300-3-33300000002i3−2i300−2i32i30000000000−i3i3i3−i3000000000000000000000000000
χ6644-4-4-2442-44-442-4-4-2-2-24022-4-4-2422-200-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ6744-4-4-2442-44-442-4-4-2-2-24022-4-4-2422-200-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ684-44-444-24422-4-4-2-4-44-2-204-2-2222-42-44-4-2-2220000000000000000004-400-220000000000-220000000000000000000000000000000
χ694-44-444-24422-4-4-2-4-44-2-204-2-2222-42-4-44-2-222000000000000000000-44002-200000000002-20000000000000000000000000000000
χ704-44-44-244-2-4-42-442-4-24-20-24-22-422-4200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ714-44-44-244-2-4-42-442-4-24-20-24-22-422-4200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ724-44-4-244-24-4-4-424-42-2-240-2-24-42-42224-4-2-222000000000000000000-22004-40000000000-220000000000000000000000000000000
χ734-44-4-244-24-4-4-424-42-2-240-2-24-42-4222-44-2-2220000000000000000002-200-4400000000002-20000000000000000000000000000000
χ744-44-4-24-2-2422-42-2-42-21-20-21-22-122-124-411-1-10003i−3i00003i−3i3i−3i00000-2200-2200000000001-1000000003i−3i000000000000000000000
χ754-44-4-24-2-2422-42-2-42-21-20-21-22-122-124-411-1-1000−3i3i0000−3i3i−3i3i00000-2200-2200000000001-100000000−3i3i000000000000000000000
χ764-44-4-24-2-2422-42-2-42-21-20-21-22-122-12-4411-1-10003i−3i00003i−3i3i−3i000002-2002-20000000000-1100000000−3i3i000000000000000000000
χ774-44-4-24-2-2422-42-2-42-21-20-21-22-122-12-4411-1-1000−3i3i0000−3i3i−3i3i000002-2002-20000000000-11000000003i−3i000000000000000000000
χ784-4-44444-4-4-44-44-44-44440-4-4-44-4-444-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-42-2-4424-44-2-20-422-2224-2-400-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ804-4-4444-2-4-42-2-4424-44-2-20-422-2224-2-400-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ814-4-444-24-42-4424-4-2-4-24-202-42-2-42-24200-22-2200000000000000000000000000−2i32i3000000000000000000−2i32i30000000000000000000
χ824-4-444-24-42-4424-4-2-4-24-202-42-2-42-24200-22-22000000000000000000000000002i3−2i30000000000000000002i3−2i30000000000000000000
χ834-4-44-2442-4-44-4-2-442-2-24022-442-4-2-2200-22-22000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ844-4-44-2442-4-44-4-2-442-2-24022-442-4-2-2200-22-220000000000000000000000000000−2323000000000000000000−232300000000000000000
χ854-4-44-2-2422-442-2-4-221-2-20-122-2221-2-1001-11-100000003i−3i3i−3i−3i3i0000000000000−2i32i323−230000000000000000i3−i3−3300000000000000000
χ864-4-44-2-2422-442-2-4-221-2-20-122-2221-2-1001-11-100000003i−3i3i−3i−3i3i00000000000002i3−2i3−23230000000000000000−i3i33−300000000000000000
χ874-4-44-2-2422-442-2-4-221-2-20-122-2221-2-1001-11-10000000−3i3i−3i3i3i−3i0000000000000−2i32i3−23230000000000000000i3−i33−300000000000000000
χ884-4-44-2-2422-442-2-4-221-2-20-122-2221-2-1001-11-10000000−3i3i−3i3i3i−3i00000000000002i3−2i323−230000000000000000−i3i3−3300000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4222822222222200-1-1-1-1-4-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222200-1-1-1-1444-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-44-8-44844-8-4-42-404-2442-44-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48448-8-44-84-42-4-40-2444-4-4-242002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-44-4444-42220-2-2-2-222-2-2200-111-1000006-600-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-44-4444-42220-2-2-2-222-2-2200-111-100000-660033-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-48-4444-8-44-8-4-420-4-42-24-24440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-4-8-8448442-4-402-4-4444-24-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4-44444-4442220222-2-2-2-2-2-200-1-1110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-44444-4442220222-2-2-2-2-2-200-1-111000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844-4484-4-8-4-42044-224-2-4-44002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-84-4-8-4484-42-404-24-4-24-424002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-442220-2-2-22-2-222-200-11-1100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-442220-2-2-22-2-222-200-11-110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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