Finite Group Databasebeta

← Group #10713266

Character table — Group #10713266

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order1222234444666886688812121212242424244488121212122424242424244488121212122424242416161616161616168888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9111-1-11-11-111-1-1111-1-11-1-11-1111-1-1i−ii−iii−i−i1-1ii−i−ii−i1-1ii−i−i11-1-111-1-1ii−i−ii−i1-1
χ10111-1-11-11-111-1-1111-1-11-1-11-1111-1-1i−ii−iii−i−i1-1ii−i−ii−i1-1ii−i−i11-1-1-1-111−i−iii−ii-11
χ11111-1-11-11-111-1-1111-1-11-1-11-1111-1-1i−ii−iii−i−i1-1ii−i−i−ii-11−i−iii-1-11111-1-1ii−i−i−ii-11
χ12111-1-11-11-111-1-1111-1-11-1-11-1111-1-1i−ii−iii−i−i1-1ii−i−i−ii-11−i−iii-1-111-1-111−i−iiii−i1-1
χ13111-1-11-11-111-1-1111-1-11-1-11-1111-1-1−ii−ii−i−iii1-1−i−iiii−i-11ii−i−i-1-11111-1-1−i−iiii−i-11
χ14111-1-11-11-111-1-1111-1-11-1-11-1111-1-1−ii−ii−i−iii1-1−i−iiii−i-11ii−i−i-1-111-1-111ii−i−i−ii1-1
χ15111-1-11-11-111-1-1111-1-11-1-11-1111-1-1−ii−ii−i−iii1-1−i−iii−ii1-1−i−iii11-1-111-1-1−i−iii−ii1-1
χ16111-1-11-11-111-1-1111-1-11-1-11-1111-1-1−ii−ii−i−iii1-1−i−iii−ii1-1−i−iii11-1-1-1-111ii−i−ii−i-11
χ172222222222222-2-222-2-2-22222-2-2-2-222-2-22222-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-222-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ1922222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-11111000000000000
χ2222222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-1000000000000
χ2322222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-1111122-2-2-1-1-1-11111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ2422222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-1111122-2-2-1-1-1-11111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ2522222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-222111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ2622222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-222111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ27222-2-22-22-222-2-2-2-22-22-22-22-22-2-2222i−2i−2i2i2i2i−2i−2i-22−2i−2i2i2i000000000000000000000000
χ28222-2-22-22-222-2-2-2-22-22-22-22-22-2-222−2i2i2i−2i−2i−2i2i2i-222i2i−2i−2i000000000000000000000000
χ29222-2-2-1-22-22-11122-11-22-21-11-1-1-1112i−2i2i−2i−i−iii-11−i−iii2i−2i2-2−i−iii-1-111000000000000
χ30222-2-2-1-22-22-11122-11-22-21-11-1-1-1112i−2i2i−2i−i−iii-11−i−iii−2i2i-22ii−i−i11-1-1000000000000
χ31222-2-2-1-22-22-11122-11-22-21-11-1-1-111−2i2i−2i2iii−i−i-11ii−i−i2i−2i-22−i−iii11-1-1000000000000
χ32222-2-2-1-22-22-11122-11-22-21-11-1-1-111−2i2i−2i2iii−i−i-11ii−i−i−2i2i2-2ii−i−i-1-111000000000000
χ33222-2-2-1-22-22-111-2-2-112-221-11-111-1-12i−2i−2i2i−i−iii1-1ii−i−i00003−3−33−i3i3i3−i3000000000000
χ34222-2-2-1-22-22-111-2-2-112-221-11-111-1-12i−2i−2i2i−i−iii1-1ii−i−i0000−333−3i3−i3−i3i3000000000000
χ35222-2-2-1-22-22-111-2-2-112-221-11-111-1-1−2i2i2i−2iii−i−i1-1−i−iii00003−3−33i3−i3−i3i3000000000000
χ36222-2-2-1-22-22-111-2-2-112-221-11-111-1-1−2i2i2i−2iii−i−i1-1−i−iii0000−333−3−i3i3i3−i3000000000000
χ3722-22-2222-2-22-2-222-22-2-2222-2-222-2-200000000-22000000000000000000002-22-20000
χ3822-22-2222-2-22-2-222-22-2-2222-2-222-2-200000000-2200000000000000000000-22-220000
χ3922-22-2222-2-22-2-2-2-2-2222-222-2-2-2-222000000002-200000000000000002-22-200000000
χ4022-22-2222-2-22-2-2-2-2-2222-222-2-2-2-222000000002-20000000000000000-22-2200000000
χ4122-2-222-222-222222-2-22-2-2-222-2222200000000-2-2000000000000000000002i−2i−2i2i0000
χ4222-2-222-222-222222-2-22-2-2-222-2222200000000-2-200000000000000000000−2i2i2i−2i0000
χ4322-2-222-222-2222-2-2-2-2-222-222-2-2-2-2-2000000002200000000000000002-2-2200000000
χ4422-2-222-222-2222-2-2-2-2-222-222-2-2-2-2-200000000220000000000000000-222-200000000
χ45444444-4-4-4-44440044000-4-4-4-4000000000000000000000000000000000000000000
χ4644444-2-4-4-4-4-2-2-200-2-200022220000000000000023−2323−23000000000000000000000000
χ4744444-2-4-4-4-4-2-2-200-2-2000222200000000000000−2323−2323000000000000000000000000
χ48444-4-444-44-44-4-4004-40004-44-4000000000000000000000000000000000000000000
χ49444-4-4-24-44-4-22200-22000-22-2200000000000000−2i32i32i3−2i3000000000000000000000000
χ50444-4-4-24-44-4-22200-22000-22-22000000000000002i3−2i3−2i32i3000000000000000000000000
χ5144-44-44-4-4444-4-400-44000-4-444000000000000000000000000000000000000000000
χ5244-44-4-244-4-4-222442-2-4-44-2-222-2-222000000002-20000000000000000000000000000
χ5344-44-4-244-4-4-222-4-42-244-4-2-22222-2-200000000-220000000000000000000000000000
χ5444-44-4-2-4-444-222002-200022-2-20000000023−2323−23000000000000000000000000000000
χ5544-44-4-2-4-444-222002-200022-2-200000000−2323−2323000000000000000000000000000000
χ5644-4-4444-4-4444400-4-40004-4-44000000000000000000000000000000000000000000
χ5744-4-44-24-4-44-2-2-20022000-222-200000000−2i32i32i3−2i3000000000000000000000000000000
χ5844-4-44-24-4-44-2-2-20022000-222-2000000002i3−2i3−2i32i3000000000000000000000000000000
χ5944-4-44-2-444-4-2-2-244224-4-42-2-22-2-2-2-200000000220000000000000000000000000000
χ6044-4-44-2-444-4-2-2-2-4-422-4442-2-22222200000000-2-20000000000000000000000000000
χ618-800080000-800−4i24i2000000000−4i24i20000000000000000000000000000000000000000
χ628-800080000-8004i2−4i20000000004i2−4i20000000000000000000000000000000000000000
χ638-8000-400004−4i34i3−4i24i20000000002i2−2i226−2600000000000000000000000000000000000000
χ648-8000-400004−4i34i34i2−4i2000000000−2i22i2−262600000000000000000000000000000000000000
χ658-8000-4000044i3−4i3−4i24i20000000002i2−2i2−262600000000000000000000000000000000000000
χ668-8000-4000044i3−4i34i2−4i2000000000−2i22i226−2600000000000000000000000000000000000000

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