Finite Group Databasebeta

← Group #10868284

Character table — Group #10868284

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212244444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ5111111111111111111111111-1-1111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-111-11111-1-111-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-1111
χ7111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1111-1-11111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-111-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1111-1-111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-111111-1-1-1-111-1
χ17222222222-2-2-2-22222222000022-2-2-22222-2-200000000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222000022-2-2-22222-2-200000000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-22000000002200000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000220000000000000000-2-2-2-22200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-22222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-22222-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-2-222-22-222-2-2222-2-2-22i2i−2i−2i002-2-2000020002i−2i2-200002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-2-2-222-22-222-2-2222-2-2-22i2i−2i−2i002-2-200002000−2i2i-2200002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-2-2-222-22-222-2-2222-2-2-2−2i−2i2i2i002-2-2000020002i−2i-220000−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3222-2-2-222-22-222-2-2222-2-2-2−2i−2i2i2i002-2-200002000−2i2i2-20000−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3322-2-2-222-2-1-222-21-1-1-11112i2i−2i−2i00-111−i3−i3i3i3-10002i−2i2-200−i3i3−i−iii33−3−3-1-111−i3−i3i3i300000003−3−ii000000000000
χ3422-2-2-222-2-1-222-21-1-1-11112i2i−2i−2i00-111−i3−i3i3i3-1000−2i2i-2200−i3i3−i−iii33−3−311-1-1i3i3−i3−i30000000−33i−i000000000000
χ3522-2-2-222-2-1-222-21-1-1-11112i2i−2i−2i00-111i3i3−i3−i3-10002i−2i2-200i3−i3−i−iii−3−333-1-111i3i3−i3−i30000000−33−ii000000000000
χ3622-2-2-222-2-1-222-21-1-1-11112i2i−2i−2i00-111i3i3−i3−i3-1000−2i2i-2200i3−i3−i−iii−3−33311-1-1−i3−i3i3i300000003−3i−i000000000000
χ3722-2-2-222-2-1-222-21-1-1-1111−2i−2i2i2i00-111−i3−i3i3i3-10002i−2i-2200−i3i3ii−i−i−3−33311-1-1i3i3−i3−i300000003−3−ii000000000000
χ3822-2-2-222-2-1-222-21-1-1-1111−2i−2i2i2i00-111−i3−i3i3i3-1000−2i2i2-200−i3i3ii−i−i−3−333-1-111−i3−i3i3i30000000−33i−i000000000000
χ3922-2-2-222-2-1-222-21-1-1-1111−2i−2i2i2i00-111i3i3−i3−i3-10002i−2i-2200i3−i3ii−i−i33−3−311-1-1−i3−i3i3i30000000−33−ii000000000000
χ4022-2-2-222-2-1-222-21-1-1-1111−2i−2i2i2i00-111i3i3−i3−i3-1000−2i2i2-200i3−i3ii−i−i33−3−3-1-111i3i3−i3−i300000003−3i−i000000000000
χ412-222-2-22-2222-2-2-22-2-22-22000000-22-20000202-20000000000002-22-2000000002i−2i002i−2i00000000002i−2i00000
χ422-222-2-22-2222-2-2-22-2-22-22000000-22-20000202-20000000000002-22-200000000−2i2i00−2i2i0000000000−2i2i00000
χ432-222-2-22-2222-2-2-22-2-22-22000000-22-2000020-22000000000000-22-22000000002i−2i002i−2i0000000000−2i2i00000
χ442-222-2-22-2222-2-2-22-2-22-22000000-22-2000020-22000000000000-22-2200000000−2i2i00−2i2i00000000002i−2i00000
χ452-222-2-22-22-2-222-22-2-22-222i−2i2i−2i002-220000-2000000000002i−2i2i−2i0000000000002i−2i00−2i2i000000002-20000000
χ462-222-2-22-22-2-222-22-2-22-222i−2i2i−2i002-220000-2000000000002i−2i2i−2i000000000000−2i2i002i−2i00000000-220000000
χ472-222-2-22-22-2-222-22-2-22-22−2i2i−2i2i002-220000-200000000000−2i2i−2i2i0000000000002i−2i00−2i2i00000000-220000000
χ482-222-2-22-22-2-222-22-2-22-22−2i2i−2i2i002-220000-200000000000−2i2i−2i2i000000000000−2i2i002i−2i000000002-20000000
χ492-2-2-22-22222-22-222-2-2-22-22-2-220022-20000-2000000000002-2-220000000000000000000000002i−2i00002i−2i000
χ502-2-2-22-22222-22-222-2-2-22-22-2-220022-20000-2000000000002-2-22000000000000000000000000−2i2i0000−2i2i000
χ512-2-2-22-22222-22-222-2-2-22-2-222-20022-20000-200000000000-222-20000000000000000000000002i−2i0000−2i2i000
χ522-2-2-22-22222-22-222-2-2-22-2-222-20022-20000-200000000000-222-2000000000000000000000000−2i2i00002i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044222-2-2-2-22-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222400000000-2-2000000000000000000000000000000000000000
χ55444-44-4-4-440000-4-44-444-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ56444-44-4-4-440000-4-44-444-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ57444-44-4-4-4-2000022-22-2-2200000000023−2323−230000000022−2200000000006−66−6−22−2200000000000000000000000
χ58444-44-4-4-4-2000022-22-2-2200000000023−2323−2300000000−22220000000000−66−662−22−200000000000000000000000
χ59444-44-4-4-4-2000022-22-2-22000000000−2323−23230000000022−220000000000−66−66−22−2200000000000000000000000
χ60444-44-4-4-4-2000022-22-2-22000000000−2323−232300000000−222200000000006−66−62−22−200000000000000000000000
χ6144-44-4-4-44400004-44-4-4-4400004i−4i0004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44400004-44-4-4-440000−4i4i000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44-20000-22-2222-200004i−4i000−2i2i2i−2i000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ6444-44-4-4-44-20000-22-2222-200004i−4i000−2i2i2i−2i00000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ6544-44-4-4-44-20000-22-2222-20000−4i4i0002i−2i−2i2i000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ6644-44-4-4-44-20000-22-2222-20000−4i4i0002i−2i−2i2i00000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ6744-4-4-444-444-4-44-4444-4-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ6844-4-4-444-4-24-4-442-2-2-22220000002-2-2−2i3−2i32i32i320000000002i3−2i3000000000000000000000000000000000000000
χ6944-4-4-444-4-24-4-442-2-2-22220000002-2-22i32i3−2i3−2i32000000000−2i32i3000000000000000000000000000000000000000
χ704-444-4-44-4-244-4-42-222-22-20000002-220000-204-4000000000000-22-220000000000000000000000000000000
χ714-444-4-44-4-244-4-42-222-22-20000002-220000-20-440000000000002-22-20000000000000000000000000000000
χ724-444-4-44-4-2-4-4442-222-22-24i−4i4i−4i00-22-20000200000000000−2i2i−2i2i00000000000000000000000000000000000
χ734-444-4-44-4-2-4-4442-222-22-2−4i4i−4i4i00-22-200002000000000002i−2i2i−2i00000000000000000000000000000000000
χ744-44-4-44-44400004-4-444-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ754-44-4-44-44400004-4-444-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ764-4-4444-4-440000-4-4-44-44400000000000000000000000000000000000000000004i−4i0000000000000000000
χ774-4-4444-4-440000-4-4-44-4440000000000000000000000000000000000000000000−4i4i0000000000000000000
χ784-4-4-44-4444-44-4444-4-4-44-4000000-4-440000400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-44-4-2-2222-224-4-4400-2-220000200000000000-222-200000000000000000000000000000000000
χ804-4-4-44-444-24-44-4-2-2222-22-444-400-2-2200002000000000002-2-2200000000000000000000000000000000000
χ814-4-4-44-444-2-44-44-2-2222-2200000022-20000-200000000000000023−23−23230000000000000000000000000000000
χ824-4-4-44-444-2-44-44-2-2222-2200000022-20000-2000000000000000−232323−230000000000000000000000000000000
χ838-88-8-88-88-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000

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