Finite Group Databasebeta

← Group #10712394

Character table — Group #10712394

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222222222224444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order122223444468812124444666888121212242424248812121212242424242424244466121212121212222244441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111-1-111-11-1111-1-1ii−i−i1-1-11-1-11-1111-1-1i−iii−i−iii−i−i1-11-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111-1-111-11-1111-1-1ii−i−i1-1-11-1-11-1111-1-1i−iii−i−iii−i−i1-11-1i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ11111-1-111-11-1111-1-1ii−i−i1-1-11-1-11-1111-1-1i−iii−i−iii−i−i1-1-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ12111-1-111-11-1111-1-1ii−i−i1-1-11-1-11-1111-1-1i−iii−i−iii−i−i1-1-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ13111-1-111-11-1111-1-1−i−iii1-1-11-1-11-1111-1-1−ii−i−iii−i−iii1-11-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ14111-1-111-11-1111-1-1−i−iii1-1-11-1-11-1111-1-1−ii−i−iii−i−iii1-11-1−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ15111-1-111-11-1111-1-1−i−iii1-1-11-1-11-1111-1-1−ii−i−iii−i−iii1-1-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ16111-1-111-11-1111-1-1−i−iii1-1-11-1-11-1111-1-1−ii−i−iii−i−iii1-1-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222-2-2222222222-2-2-2222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000
χ19222222-2-2-2-2200-2-22-22-2222000-2-2-20000002-22-2000000000000000000000000002−22−22−22−2
χ20222222-2-2-2-2200-2-22-22-2222000-2-2-20000002-22-200000000000000000000000000−22−22−22−22
χ21222222-2-2-2-2200-2-2-22-22222000-2-2-2000000-22-22000000000000000000000000002−22−2−22−22
χ22222222-2-2-2-2200-2-2-22-22222000-2-2-2000000-22-2200000000000000000000000000−22−222−22−2
χ2322222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2422222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2522222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-2-211111111-1-122-2-2-1-1-1-111110000000000000000
χ2622222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-2-211111111-1-1-2-2221111-1-1-1-10000000000000000
χ2722222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-2-2-1-1-1-11111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-2-2-1-1-1-11111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-11111221111-1-1-1-1110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-11111221111-1-1-1-1110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ31222-2-222-22-22-2-2-2-22i2i−2i−2i2-2-2-2222-22-2-222−2i2i2i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000
χ32222-2-222-22-22-2-2-2-2−2i−2i2i2i2-2-2-2222-22-2-2222i−2i−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000
χ33222-2-22-22-22200222i−2i−2i2i2-2-2000-22-20000002i−2i−2i2i000000000000000000000000002−2−22i2−i2−i2i2
χ34222-2-22-22-22200222i−2i−2i2i2-2-2000-22-20000002i−2i−2i2i00000000000000000000000000−222−2−i2i2i2−i2
χ35222-2-22-22-2220022−2i2i2i−2i2-2-2000-22-2000000−2i2i2i−2i000000000000000000000000002−2−22−i2i2i2−i2
χ36222-2-22-22-2220022−2i2i2i−2i2-2-2000-22-2000000−2i2i2i−2i00000000000000000000000000−222−2i2−i2−i2i2
χ37222-2-2-12-22-2-122112i2i−2i−2i-1112-2-2-11-1-1-1112i−2i−i−iii−i−iii-112-22i−2i-1-111−i−iii0000000000000000
χ38222-2-2-12-22-2-122112i2i−2i−2i-1112-2-2-11-1-1-1112i−2i−i−iii−i−iii-11-22−2i2i11-1-1ii−i−i0000000000000000
χ39222-2-2-12-22-2-12211−2i−2i2i2i-1112-2-2-11-1-1-111−2i2iii−i−iii−i−i-112-2−2i2i-1-111ii−i−i0000000000000000
χ40222-2-2-12-22-2-12211−2i−2i2i2i-1112-2-2-11-1-1-111−2i2iii−i−iii−i−i-11-222i−2i11-1-1−i−iii0000000000000000
χ41222-2-2-12-22-2-1-2-2112i2i−2i−2i-111-222-11-111-1-1−2i2i−i−iiiii−i−i1-10000−i3i3i3−i33−3−330000000000000000
χ42222-2-2-12-22-2-1-2-2112i2i−2i−2i-111-222-11-111-1-1−2i2i−i−iiiii−i−i1-10000i3−i3−i3i3−333−30000000000000000
χ43222-2-2-12-22-2-1-2-211−2i−2i2i2i-111-222-11-111-1-12i−2iii−i−i−i−iii1-10000−i3i3i3−i3−333−30000000000000000
χ44222-2-2-12-22-2-1-2-211−2i−2i2i2i-111-222-11-111-1-12i−2iii−i−i−i−iii1-10000i3−i3−i3i33−3−330000000000000000
χ4522-22-22-222-2222-2-20000-2-22-2-22-22222-2-20000000000-220000000000002-22-2000000000000
χ4622-22-22-222-2222-2-20000-2-22-2-22-22222-2-20000000000-22000000000000-22-22000000000000
χ4722-22-22-222-22-2-2-2-20000-2-2222-2-222-2-22200000000002-200000000000000002i−2i2i−2i00000000
χ4822-22-22-222-22-2-2-2-20000-2-2222-2-222-2-22200000000002-20000000000000000−2i2i−2i2i00000000
χ4922-2-222-2-222222220000-22-2-22-2-2-2222220000000000-2-20000000000002-2-22000000000000
χ5022-2-222-2-222222220000-22-2-22-2-2-2222220000000000-2-2000000000000-222-2000000000000
χ5122-2-222-2-2222-2-2220000-22-22-22-2-22-2-2-2-200000000002200000000000000002-2-2200000000
χ5222-2-222-2-2222-2-2220000-22-22-22-2-22-2-2-2-20000000000220000000000000000-222-200000000
χ5344444-2-4-4-4-4-200224-44-4-2-2-2000222000000-22-220000000000000000000000000000000000
χ5444444-2-4-4-4-4-20022-44-44-2-2-20002220000002-22-20000000000000000000000000000000000
χ55444-4-4-2-44-44-200-2-24i−4i−4i4i-2220002-22000000−2i2i2i−2i0000000000000000000000000000000000
χ56444-4-4-2-44-44-200-2-2−4i4i4i−4i-2220002-220000002i−2i−2i2i0000000000000000000000000000000000
χ5744-44-444-4-44400440000-4-440004-4-400000000000000000000000000000000000000000000
χ5844-44-4-24-4-44-200-2-2000022-2000-2220000000000−2i32i3−2i32i3000000000000000000000000000000
χ5944-44-4-24-4-44-200-2-2000022-2000-22200000000002i3−2i32i3−2i3000000000000000000000000000000
χ6044-44-4-2-444-4-24422000022-2-4-442-2-2-2-22200000000002-20000000000000000000000000000
χ6144-44-4-2-444-4-2-4-422000022-244-42-2-222-2-20000000000-220000000000000000000000000000
χ6244-4-44444-4-4400-4-40000-44-400044-400000000000000000000000000000000000000000000
χ6344-4-44-244-4-4-2002200002-22000-2-22000000000023−23−2323000000000000000000000000000000
χ6444-4-44-244-4-4-2002200002-22000-2-220000000000−232323−23000000000000000000000000000000
χ6544-4-44-2-4-444-244-2-200002-22-44-422-2-2-2-2-20000000000220000000000000000000000000000
χ6644-4-44-2-4-444-2-4-4-2-200002-224-4422-222220000000000-2-20000000000000000000000000000
χ678-800080000-842−4200000000000000042−42000000000000000000000000000000000000000000
χ688-800080000-8−4242000000000000000−4242000000000000000000000000000000000000000000
χ698-8000-40000442−4243−430000000000000−222226−260000000000000000000000000000000000000000
χ708-8000-40000442−42−43430000000000000−2222−26260000000000000000000000000000000000000000
χ718-8000-400004−424243−43000000000000022−22−26260000000000000000000000000000000000000000
χ728-8000-400004−4242−4343000000000000022−2226−260000000000000000000000000000000000000000

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