Finite Group Databasebeta

← Group #13168105

Character table — Group #13168105

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666443666121212121212121212121212122224466666612121212121222666666666121212121212121212444446612121212441212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111-1-111-1-111-1-1-111-1-111111-1111-1-1111-1-1-11-1-111-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-1-1-111111111-1-11-1-111-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-11-111-1-1-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111111-11111111-1-111-1-111111111111-11-1-1-111-1-1-1-1-11-111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-111-1-111-1-1-1-11-1-111-1-1-1-1-11-1-1-111-1-11-1-1-11-1-111-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-111-1-11-111111-1-1-1-1-1-1-1-1-111-11-111-1-111-1-1-1-1-1111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-111111111-1-11-1-111-1-1-11-1-1-11111-1-11-1111111111-1-1-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-111-1-111-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111-11-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1111111-1-1-11-1-1-1-1-111-11-1-1-111111-111-1-1-1-1-111-1-111-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1-1-1-1-1-11-111111-1-11-1111-1-1-1-11-111-1-1-1-1-1111111-1-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111-1-111-1-11-1-111-1-11111111-1-111-1-1-111-1-1-1-1-1-11-111
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-111-1-1111-1111-1-1-1-1-1-11-11111111-1-1-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111-1-1-1-1-11-1-1-1-1-1111111111-1-1-11-111-1-111-1-111-111-1
χ17222222-1-12-1222-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-12220222-1-1-1-10022002222-1-1-1-1-1-1-10-1000-1-10000020-1-10000000-100
χ18222222-1-12-1222-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-122-20-222-1-11100-2-200-2-2-22-111-1-1-1-1010001100000-20110000000100
χ19222222-1-12-1222-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2202-2-211-1-1002200-2-22-21-1-111110-1000-1-100000-20110000000100
χ20222222-1-12-1222-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-20-2-2-2111100-2-20022-2-2111111101000110000020-1-10000000-100
χ21222222-1-12-1222-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-211112-220-22211-1-100-2-200-2-22-2-1-1-1-1-11101000110000020110000000-100
χ22222222-1-12-1222-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-211112-2-20222111100220022-2-2-111-1-1110-1000-1-100000-20-1-10000000100
χ23222222-1-12-1222-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-21111-2220-2-2-2-1-1-1-100-2-20022221-1-111-1-1010001100000-20-1-10000000100
χ24222222-1-12-1222-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-21111-22-202-2-2-1-111002200-2-2-2211111-1-10-1000-1-10000020110000000-100
χ2522222-122-1222-12-12-12-12-12-1-12-1-12-122-1-1-1-122-122-1-1-1-1-1-1-1-122020-1-122002200-1-1000-1200-1-1-1-1-102-1-100-1-12000200-1-10000-1000
χ2622222-122-1222-12-12-12-12-12-1-12-1-12-122-1-1-1-122-122-1-1-1-1-1-1-1-1-2-202011-2-2002200-1-10001-2001111-102-1-100-1-1-2000-2001100001000
χ2722222-122-1222-12-12-12-12-12-1-12-1-12-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1220-20-1-12200-2-20011000-1200-1-1-1-110-2110011-2000-2001100001000
χ2822222-122-1222-12-12-12-12-12-1-12-1-12-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1-2-20-2011-2-200-2-200110001-200111110-21100112000200-1-10000-1000
χ2922222-122-1222-12-12-12-1-2-12-1-12-1-12-122-1-1-1-1-2-21-2-2111111112-20-20-1-1-2-2002200-1-10001200-1-11110-21100-1-1-2000200-1-100001000
χ3022222-122-1222-12-12-12-1-2-12-1-12-1-12-122-1-1-1-1-2-21-2-211111111-220-201122002200-1-1000-1-20011-1-110-21100-1-12000-200110000-1000
χ3122222-122-1222-12-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-2-21-2-2111111112-2020-1-1-2-200-2-200110001200-1-111-102-1-100112000-200110000-1000
χ3222222-122-1222-12-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-2-21-2-211111111-22020112200-2-20011000-1-20011-1-1-102-1-10011-2000200-1-100001000
χ332222-122222-1-1222-1-1-122-1-122-12-1-1-122-1-1-1-12-12-1-122-1-1-1-1-1-100222000022-1-1-1-12200-100-1-1000022-1-1-1-1-1-1-1022000000-1-10000-10
χ342222-122222-1-1222-1-1-122-1-122-12-1-1-122-1-1-1-12-12-1-122-1-1-1-1-1-100-22-20000-2-2-1-11122001001100002-2-1-1-111-1-10-2-200000011000010
χ352222-122222-1-1222-1-1-122-1-122-12-1-1-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-1002-2200002211-1-1-2-200-100-1-10000-22111-1-1110-2-200000011000010
χ362222-122222-1-1222-1-1-122-1-122-12-1-1-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-100-2-2-20000-2-21111-2-200100110000-2-21111111022000000-1-10000-10
χ372222-122222-1-1222-1-1-12-2-1-122-12-1-1-122-1-1-1-1-21-211-2-2111111002-2-2000022-1-1112200-100-1-10000-2-211111-1-102-2000000110000-10
χ382222-122222-1-1222-1-1-12-2-1-122-12-1-1-122-1-1-1-1-21-211-2-211111100-2-220000-2-2-1-1-1-12200100110000-22111-1-1-1-10-22000000-1-1000010
χ392222-122222-1-1222-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-21-211-2-21111110022-20000221111-2-200-100-1-100002-2-1-1-111110-22000000-1-1000010
χ402222-122222-1-1222-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-21-211-2-211111100-2220000-2-211-1-1-2-20010011000022-1-1-1-1-11102-2000000110000-10
χ4122-2-2222-222-22-2-2-2-22220-2-22-2-2-222-22i−2i22-2-20000000000000000000000002i−2i002i−2i2-200000000000000002i−2i000002-200002i−2i0000
χ4222-2-2222-222-22-2-2-2-22220-2-22-2-2-222-22i−2i22-2-20000000000000000000000002i−2i002i−2i-2200000000000000002i−2i00000-220000−2i2i0000
χ4322-2-2222-222-22-2-2-2-22220-2-22-2-2-222-2−2i2i22-2-2000000000000000000000000−2i2i00−2i2i2-20000000000000000−2i2i000002-20000−2i2i0000
χ4422-2-2222-222-22-2-2-2-22220-2-22-2-2-222-2−2i2i22-2-2000000000000000000000000−2i2i00−2i2i-220000000000000000−2i2i00000-2200002i−2i0000
χ4544444-2-2-2-2-244-2-2-24-2-214-2-211-21-2-2-2001111-24-2-2-211-2-2111144000-2-2-2-200000000000-2-200111100000000000000000000000000
χ4644444-2-2-2-2-244-2-2-24-2-214-2-211-21-2-2-2001111-24-2-2-211-2-21111-4-40002222000000000002200-1-1-1-100000000000000000000000000
χ4744444-2-2-2-2-244-2-2-24-2-21-4-2-211-21-2-2-20011112-4222-1-122-1-1-1-14-4000-2-222000000000002-20011-1-100000000000000000000000000
χ4844444-2-2-2-2-244-2-2-24-2-21-4-2-211-21-2-2-20011112-4222-1-122-1-1-1-1-4400022-2-200000000000-2200-1-11100000000000000000000000000
χ494444-24-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2001111-2-2411-2-2-2-21111004040000-2-200-2-20000-2001100000-2000110000000000000000000
χ504444-24-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2001111-2-2411-2-2-2-2111100-40-400002200220000200-1-1000002000-1-10000000000000000000
χ514444-24-2-24-2-2-24-24-2-21-2-4-21-2-21-2-21-200111122-4-1-12222-1-1-1-10040-40000-2-200220000-20011000002000-1-10000000000000000000
χ524444-24-2-24-2-2-24-24-2-21-2-4-21-2-21-2-21-200111122-4-1-12222-1-1-1-100-40400002200-2-20000200-1-100000-2000110000000000000000000
χ534444-2-244-24-2-2-24-2-21-2-241-2-2-2-2-21-214411114-2-2-2-2-2-211111100040000000-2-200-2-200000000000-20-211001100000000000000000
χ544444-2-244-24-2-2-24-2-21-2-241-2-2-2-2-21-21-4-411114-2-2-2-2-2-2111111000-4000000022002200000000000202-1-100-1-100000000000000000
χ554444-2-244-24-2-2-24-2-21-2-2-41-2-2-2-2-21-21441111-4222222-1-1-1-1-1-1000-40000000-2-200-2-200000000000202-1-1001100000000000000000
χ564444-2-244-24-2-2-24-2-21-2-2-41-2-2-2-2-21-21-4-41111-4222222-1-1-1-1-1-10004000000022002200000000000-20-21100-1-100000000000000000
χ5744-4-444-224-2-44-42-4-44-2-20-42-22224-2-400-2-2220000000000000000000000000000004-400000000000000000000000-220000000000
χ5844-4-444-224-2-44-42-4-44-2-20-42-22224-2-400-2-222000000000000000000000000000000-44000000000000000000000002-20000000000
χ5944-4-44-24-4-24-442-42-4-24-202-4-22-42-2424i−4i-2-2220000000000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000
χ6044-4-44-24-4-24-442-42-4-24-202-4-22-42-242−4i4i-2-222000000000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000
χ6144-4-4-244-4442-2-4-4-42-2-240224-42-4-2-224i−4i-2-222000000000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000
χ6244-4-4-244-4442-2-4-4-42-2-240224-42-4-2-22−4i4i-2-2220000000000000000000000002i−2i00−4i4i0000000000000000002i−2i00000000000000000
χ6344-4-4-2-24-4-242-22-4221-2-20-12-22221-2-14i−4i11-1-100000003i−3i3i3i−3i−3i00000000000−2i2i00−2i2i000000000000003-300i−i00000000000000000
χ6444-4-4-2-24-4-242-22-4221-2-20-12-22221-2-14i−4i11-1-10000000−3i3i−3i−3i3i3i00000000000−2i2i00−2i2i00000000000000-3300i−i00000000000000000
χ6544-4-4-2-24-4-242-22-4221-2-20-12-22221-2-1−4i4i11-1-100000003i−3i3i3i−3i−3i000000000002i−2i002i−2i00000000000000-3300−ii00000000000000000
χ6644-4-4-2-24-4-242-22-4221-2-20-12-22221-2-1−4i4i11-1-10000000−3i3i−3i−3i3i3i000000000002i−2i002i−2i000000000000003-300−ii00000000000000000
χ674-44-4444-4-4-4-4-444-44444044-44-4-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-22-42-4-44-2-444-2-204-22-222-42-400-22-220000000000000000000000−2i32i300000000000−2i32i3000000000000000000000000000000
χ694-44-444-22-42-4-44-2-444-2-204-22-222-42-400-22-2200000000000000000000002i3−2i3000000000002i3−2i3000000000000000000000000000000
χ704-44-44-24-42-4-4-4-2424-24-20-242-2-422-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ714-44-44-24-42-4-4-4-2424-24-20-242-2-422-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ724-44-4-244-4-4-42244-4-2-2-240-2-2-442-422200-22-220000000000000000000000000023−2300000000000000000023−230000000000000000000
χ734-44-4-244-4-4-42244-4-2-2-240-2-2-442-422200-22-2200000000000000000000000000−2323000000000000000000−23230000000000000000000
χ744-44-4-24-22-42224-2-4-2-21-20-212-2-122-12001-11-10003i−3i00003i−3i3i−3i000000000−2i32i30023−230000000i3−i3000000000−330000000000000000000
χ754-44-4-24-22-42224-2-4-2-21-20-212-2-122-12001-11-10003i−3i00003i−3i3i−3i0000000002i3−2i300−23230000000−i3i30000000003−30000000000000000000
χ764-44-4-24-22-42224-2-4-2-21-20-212-2-122-12001-11-1000−3i3i0000−3i3i−3i3i000000000−2i32i300−23230000000i3−i30000000003−30000000000000000000
χ774-44-4-24-22-42224-2-4-2-21-20-212-2-122-12001-11-1000−3i3i0000−3i3i−3i3i0000000002i3−2i30023−230000000−i3i3000000000−330000000000000000000
χ784-4-444444-4-44-4-4-44-44440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-2-424-4-424-44-2-20-4222-2-2-42400-222-200000000000000000000−2i32i300000000000000000−2i32i300000000000000000000000000
χ804-4-4444-2-2-424-4-424-44-2-20-4222-2-2-42400-222-2000000000000000000002i3−2i3000000000000000002i3−2i300000000000000000000000000
χ814-4-444-2442-44-42-4-2-4-24-202-4224-22-4-200-222-2000000000000000000−2i32i300000000000000000−2i32i30000000000000000000000000000
χ824-4-444-2442-44-42-4-2-4-24-202-4224-22-4-200-222-20000000000000000002i3−2i3000000000000000002i3−2i30000000000000000000000000000
χ834-4-444-2-2-2224-422-2-4-2-21022-1-1-2122-2001-1-11000003-3003-3-3300000−2i32i3−2i32i3000000000000000i3−i3i3−i300000000000000000000000000
χ844-4-444-2-2-2224-422-2-4-2-21022-1-1-2122-2001-1-11000003-3003-3-33000002i3−2i32i3−2i3000000000000000−i3i3−i3i300000000000000000000000000
χ854-4-444-2-2-2224-422-2-4-2-21022-1-1-2122-2001-1-1100000-3300-333-300000−2i32i32i3−2i3000000000000000i3−i3−i3i300000000000000000000000000
χ864-4-444-2-2-2224-422-2-4-2-21022-1-1-2122-2001-1-1100000-3300-333-3000002i3−2i3−2i32i3000000000000000−i3i3i3−i300000000000000000000000000
χ874-4-44-2444-4-4-22-4-442-2-24022-4-4-2422-200-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ884-4-44-2444-4-4-22-4-442-2-24022-4-4-2422-200-222-200000000000000000000000000000000000000000000000000000000000−2323000000
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
χ9188-8-88-4-44-4-4-88444-8-4-420442-24-2-4-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-448-44-4-84-84-42-404-2-44-24-4240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-44-444442220-2-22-2-2-222-200-1-11100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-44-444442220-2-22-2-2-222-200-1-1110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4444-8-8-4-448-4-420-4-4-224-2444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-84-844-484-42-4-402-44-444-24-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444444-4-44-4222022-22-2-2-2-2-200-11-110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444444-4-44-4222022-22-2-2-2-2-200-11-11000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-4-84-44-8484-42-404-2442-44-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4884-8-444-8-442-4-40-2444-4-4-242002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-444-4444-442220-2-2-2-222-2-2200-111-1000006-600-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-444-4444-442220-2-2-2-222-2-2200-111-100000-66003-3-33000000000000000000000000000000000000000000000000000000

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