Finite Group Databasebeta

← Group #10712367

Character table — Group #10712367

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222344446668866888121212122424242444441616161624244848484848484848444424661212121212122244881616161644
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ9111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iii−i−i1-111-1-1ii−i−i1-11-1i−i11-1-1i−i
χ10111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i−i−iii1-111-1-1ii−i−i-11-11−ii-1-111−ii
χ11111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiiiii−i−i-11-1-111ii−i−i1-11-1i−i-1-111−ii
χ12111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiii−i−iii-11-1-111ii−i−i-11-11−ii11-1-1i−i
χ13111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−iii−i−i-11-1-111−i−iii-11-11i−i11-1-1−ii
χ14111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i−i−iii-11-1-111−i−iii1-11-1−ii-1-111i−i
χ15111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1−i−iii−i−iii11−i−i−i−iiiiiii−i−i1-111-1-1−i−iii-11-11i−i-1-111i−i
χ16111-1-111-11-1111-1-1-1-11-111-1-11-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−iii1-111-1-1−i−iii1-11-1−ii11-1-1−ii
χ172222222222222-2-222-2-2-22222-2-2-2-200000000-2-200000000222200000000000000-2-2000000
χ182222222222222-2-222-2-2-22222-2-2-2-200000000-2-200000000-2-2-2-20000000000000022000000
χ19222222-2-2-2-22220022000-2-2-2-2000000002−22−20022−2−222−2−22-22-200000000000000002−22−200
χ20222222-2-2-2-22220022000-2-2-2-2000000002−22−20022−2−222−2−2-22-220000000000000000−22−2200
χ21222222-2-2-2-22220022000-2-2-2-200000000−22−2200−2−222−2−2222-22-20000000000000000−22−2200
χ22222222-2-2-2-22220022000-2-2-2-200000000−22−2200−2−222−2−222-22-2200000000000000002−22−200
χ2322222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2422222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-21111-1-1-1-1000000000000
χ2522222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2622222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ27222-2-222-22-222222-2-2-22-22-2-22222200000000-2-2000000002i2i−2i−2i00000000000000−2i2i000000
χ28222-2-222-22-222222-2-2-22-22-2-22222200000000-2-200000000−2i−2i2i2i000000000000002i−2i000000
χ29222-2-22-22-2222200-2-2000-222-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i22i−2i−2i2i0000000000000000−222−200
χ30222-2-22-22-2222200-2-2000-222-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i00000000000000002−2−2200
χ31222-2-22-22-2222200-2-2000-222-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i22i−2i−2i2i00000000000000002−2−2200
χ32222-2-22-22-2222200-2-2000-222-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i0000000000000000−222−200
χ33222-2-2-12-22-2-1-1-1-2-2112-22-111-111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ34222-2-2-12-22-2-1-1-1-2-2112-22-111-111112i2i−2i−2i−2i−2i2i2i-1-1iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ35222-2-2-12-22-2-1-1-1-2-2112-22-111-11111−2i−2i2i2i2i2i−2i−2i-1-1−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ36222-2-2-12-22-2-1-1-1-2-2112-22-111-11111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ3722-22-22-2-222-2-2222-222-2-2-22-22-2-2222-22-200002-20000000000000000002-22-2000000000000
χ3822-22-22-2-222-2-2222-222-2-2-22-22-2-222-22-2200002-2000000000000000000-22-22000000000000
χ3922-22-22-2-222-2-22-2-2-22-222-22-2222-2-200000000-22000000000000000000000022-2-200000000
χ4022-22-22-2-222-2-22-2-2-22-222-22-2222-2-200000000-220000000000000000000000-2-22200000000
χ4122-22-2-1-2-22211-1221-12-2-21-11-111-1-12-22-20000-11−i3i3−i3i3−i3i3−i3i3000000−i3i3−i3i3-11-11000000000000
χ4222-22-2-1-2-22211-1221-12-2-21-11-111-1-12-22-20000-11i3−i3i3−i3i3−i3i3−i3000000i3−i3i3−i3-11-11000000000000
χ4322-22-2-1-2-22211-1221-12-2-21-11-111-1-1-22-220000-11−i3i3−i3i3−i3i3−i3i3000000i3−i3i3−i31-11-1000000000000
χ4422-22-2-1-2-22211-1221-12-2-21-11-111-1-1-22-220000-11i3−i3i3−i3i3−i3i3−i3000000−i3i3−i3i31-11-1000000000000
χ4522-2-222-222-2-2-22222-2-2-22-2-222-2-22200000000-2200000000000000000000002-2-2200000000
χ4622-2-222-222-2-2-22222-2-2-22-2-222-2-22200000000-220000000000000000000000-222-200000000
χ4722-2-222-222-2-2-22-2-22-222-2-2-22222-2-22i−2i−2i2i00002-20000000000000000002i−2i−2i2i000000000000
χ4822-2-222-222-2-2-22-2-22-222-2-2-22222-2-2−2i2i2i−2i00002-2000000000000000000−2i2i2i−2i000000000000
χ4922-2-22-1-222-211-1-2-2-1122-211-1-1-1-1112i−2i−2i2i0000-113−33−3−33−33000000−i3i3i3−i3−iii−i000000000000
χ5022-2-22-1-222-211-1-2-2-1122-211-1-1-1-1112i−2i−2i2i0000-11−33−333−33−3000000i3−i3−i3i3−iii−i000000000000
χ5122-2-22-1-222-211-1-2-2-1122-211-1-1-1-111−2i2i2i−2i0000-113−33−3−33−33000000i3−i3−i3i3i−i−ii000000000000
χ5222-2-22-1-222-211-1-2-2-1122-211-1-1-1-111−2i2i2i−2i0000-11−33−333−33−3000000−i3i3i3−i3i−i−ii000000000000
χ5344444-24444-2-2-2-4-4-2-2-4-4-4-2-2-2-2222200000000220000000000000000000000000000000000
χ5444444-2-4-4-4-4-2-2-200-2-200022220000000022−2222−2200−2−222−2−22200000000000000000000000000
χ5544444-2-4-4-4-4-2-2-200-2-2000222200000000−2222−22220022−2−222−2−200000000000000000000000000
χ56444-4-4-24-44-4-2-2-24422-44-4-222-2-2-2-2-200000000220000000000000000000000000000000000
χ57444-4-4-2-44-44-2-2-200220002-2-2200000000−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ58444-4-4-2-44-44-2-2-200220002-2-22000000002i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ5944-44-4444-4-4-4-4400-440004-44-4000000000000000000000000000000000000000000000000
χ6044-44-4-244-4-422-2002-2000-22-2200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ6144-44-4-244-4-422-2002-2000-22-2200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ6244-44-4-2-4-44422-2-4-42-2-4442-22-2-2-222000000002-20000000000000000000000000000000000
χ6344-4-4444-4-44-4-44004-400044-4-4000000000000000000000000000000000000000000000000
χ6444-4-44-24-4-4422-200-22000-2-222000000000000006−6−66−666−600000000000000000000000000
χ6544-4-44-24-4-4422-200-22000-2-22200000000000000−666−66−6−6600000000000000000000000000
χ6644-4-44-2-444-422-244-22-4-4422-2-222-2-2000000002-20000000000000000000000000000000000
χ678-80008000000-8−4i24i200000000000−4i24i200000000000000000000000000000000000000000000
χ688-80008000000-84i2−4i2000000000004i2−4i200000000000000000000000000000000000000000000
χ698-8000-40000−4i34i34−4i24i200000000026−262i2−2i200000000000000000000000000000000000000000000
χ708-8000-40000−4i34i344i2−4i2000000000−2626−2i22i200000000000000000000000000000000000000000000
χ718-8000-400004i3−4i34−4i24i2000000000−26262i2−2i200000000000000000000000000000000000000000000
χ728-8000-400004i3−4i344i2−4i200000000026−26−2i22i200000000000000000000000000000000000000000000

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