Finite Group Databasebeta

← Group #10868089

Character table — Group #10868089

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-11-1-11111-1-11
χ1011111111111111111111-1-11111111-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-111-1-1-1-111-1
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111111-1-111-1
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-111-1-1-1-1-111-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1-1-1111111-1-1-1
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-111111-1-111-1-1-1
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1111
χ17222222222-2-2-2-22222222220000-2-2-22222-20000-20000-2-2000000000000000022-2-2220000000-2000000000
χ18222222222-2-2-2-22222222220000-2-2-22222-20000-20000-2-20000000000000000-2-222-2-200000002000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20000200002200000000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-2-2-22200000002000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-222-222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-22-22-22-222-2-2222-2-2-2002i2i−2i−2i2-2-200002002i−2i02-200002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-2-22-22-22-222-2-2222-2-2-2002i2i−2i−2i2-2-20000200−2i2i0-2200002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-2-22-22-22-222-2-2222-2-2-200−2i−2i2i2i2-2-200002002i−2i0-220000−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3222-2-22-22-22-222-2-2222-2-2-200−2i−2i2i2i2-2-20000200−2i2i02-20000−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3322-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-111−i3−i3i3i3-1002i−2i02-200−i3i3−i−iii33−3−3-1-111−i3−i3i3i300000003−3−ii000000000000
χ3422-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-111−i3−i3i3i3-100−2i2i0-2200−i3i3−i−iii33−3−311-1-1i3i3−i3−i30000000−33i−i000000000000
χ3522-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-111i3i3−i3−i3-1002i−2i02-200i3−i3−i−iii−3−333-1-111i3i3−i3−i30000000−33−ii000000000000
χ3622-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-111i3i3−i3−i3-100−2i2i0-2200i3−i3−i−iii−3−33311-1-1−i3−i3i3i300000003−3i−i000000000000
χ3722-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-111−i3−i3i3i3-1002i−2i0-2200−i3i3ii−i−i−3−33311-1-1i3i3−i3−i300000003−3−ii000000000000
χ3822-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-111−i3−i3i3i3-100−2i2i02-200−i3i3ii−i−i−3−333-1-111−i3−i3i3i30000000−33i−i000000000000
χ3922-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-111i3i3−i3−i3-1002i−2i0-2200i3−i3ii−i−i33−3−311-1-1−i3−i3i3i30000000−33−ii000000000000
χ4022-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-111i3i3−i3−i3-100−2i2i02-200i3−i3ii−i−i33−3−3-1-111i3i3−i3−i300000003−3i−i000000000000
χ412-22-222-2-2222-2-2-22-2-22-22000000-22-2000022-200000000000002-22-200000000002i−2i2i−2i00000000002i−2i00000
χ422-22-222-2-2222-2-2-22-2-22-22000000-22-2000022-200000000000002-22-20000000000−2i2i−2i2i0000000000−2i2i00000
χ432-22-222-2-2222-2-2-22-2-22-22000000-22-200002-220000000000000-22-2200000000002i−2i2i−2i0000000000−2i2i00000
χ442-22-222-2-2222-2-2-22-2-22-22000000-22-200002-220000000000000-22-220000000000−2i2i−2i2i00000000002i−2i00000
χ452-22-222-2-22-2-222-22-2-22-22002i−2i2i−2i2-220000-2000000000002i−2i2i−2i000000000000002i−2i−2i2i000002-20000000000
χ462-22-222-2-22-2-222-22-2-22-22002i−2i2i−2i2-220000-2000000000002i−2i2i−2i00000000000000−2i2i2i−2i00000-220000000000
χ472-22-222-2-22-2-222-22-2-22-2200−2i2i−2i2i2-220000-200000000000−2i2i−2i2i000000000000002i−2i−2i2i00000-220000000000
χ482-22-222-2-22-2-222-22-2-22-2200−2i2i−2i2i2-220000-200000000000−2i2i−2i2i00000000000000−2i2i2i−2i000002-20000000000
χ492-2-222-2-2222-22-222-2-2-22-2002-2-2222-20000-2000000000002-2-22000000000000000000000000002i−2i00002i−2i0
χ502-2-222-2-2222-22-222-2-2-22-2002-2-2222-20000-2000000000002-2-2200000000000000000000000000−2i2i0000−2i2i0
χ512-2-222-2-2222-22-222-2-2-22-200-222-222-20000-200000000000-222-2000000000000000000000000002i−2i0000−2i2i0
χ522-2-222-2-2222-22-222-2-2-22-200-222-222-20000-200000000000-222-200000000000000000000000000−2i2i00002i−2i0
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ554444-4-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000022−22000
χ564444-4-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000−2222000
χ5744-4-44-44-444-4-44-4444-4-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-24-4-442-2-2-22220000002-2-2−2i3−2i32i32i320000000002i3−2i3000000000000000000000000000000000000000
χ5944-4-44-44-4-24-4-442-2-2-22220000002-2-22i32i3−2i3−2i32000000000−2i32i3000000000000000000000000000000000000000
χ6044-4-4-44-4440000-4-44-4-444000000000000000000000000000000000000000004-4000000000000000000000
χ6144-4-4-44-4440000-4-44-4-44400000000000000000000000000000000000000000-44000000000000000000000
χ624-44-444-4-4-244-4-42-222-22-20000002-220000-24-40000000000000-22-220000000000000000000000000000000
χ634-44-444-4-4-244-4-42-222-22-20000002-220000-2-4400000000000002-22-20000000000000000000000000000000
χ644-44-444-4-4-2-4-4442-222-22-2004i−4i4i−4i-22-20000200000000000−2i2i−2i2i00000000000000000000000000000000000
χ654-44-444-4-4-2-4-4442-222-22-200−4i4i−4i4i-22-200002000000000002i−2i2i−2i00000000000000000000000000000000000
χ664-44-4-4-44440000-4-4-4444-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ674-44-4-4-44440000-4-4-4444-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ684-44-4-4-444-20000222-2-2-2200000000023−2323−230000000022−2200000000006−66−6−22−2200000000000000000000000
χ694-44-4-4-444-20000222-2-2-2200000000023−2323−2300000000−22220000000000−66−662−22−200000000000000000000000
χ704-44-4-4-444-20000222-2-2-22000000000−2323−23230000000022−220000000000−66−66−22−2200000000000000000000000
χ714-44-4-4-444-20000222-2-2-22000000000−2323−232300000000−222200000000006−66−62−22−200000000000000000000000
χ724-4-444-4-444-44-4444-4-4-44-4000000-4-440000400000000000000000000000000000000000000000000000000
χ734-4-444-4-44-24-44-4-2-2222-22004-4-44-2-220000200000000000-222-200000000000000000000000000000000000
χ744-4-444-4-44-24-44-4-2-2222-2200-444-4-2-2200002000000000002-2-2200000000000000000000000000000000000
χ754-4-444-4-44-2-44-44-2-2222-2200000022-20000-200000000000000023−23−23230000000000000000000000000000000
χ764-4-444-4-44-2-44-44-2-2222-2200000022-20000-2000000000000000−232323−230000000000000000000000000000000
χ774-4-44-444-4400004-4-44-4-444i−4i00000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ784-4-44-444-4400004-4-44-4-44−4i4i0000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-20000-222-222-24i−4i0000000−2i2i2i−2i000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ804-4-44-444-4-20000-222-222-24i−4i0000000−2i2i2i−2i00000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ814-4-44-444-4-20000-222-222-2−4i4i00000002i−2i−2i2i000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ824-4-44-444-4-20000-222-222-2−4i4i00000002i−2i−2i2i00000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ838888-8-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-4000044-444-4-40000000000000000000000000000000000000000000000000000000000000000

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