Finite Group Databasebeta

← Group #10710929

Character table — Group #10710929

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122223444468812126668881212122424242422441616161624244848484848484848224444661212121212124444881616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ9111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-11-11-1ii−i−i11iiii−i−i−i−i1-11-1i−i1-11-1ii−i−i11-1-11-1ii−i−ii−i
χ10111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-11-11-1ii−i−i11iiii−i−i−i−i-11-11i−i1-11-1ii−i−i-1-111-11−i−iii−ii
χ11111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-11-11-1−i−iii11−i−i−i−iiiii1-11-1−ii1-11-1−i−iii11-1-11-1−i−iii−ii
χ12111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-11-11-1−i−iii11−i−i−i−iiiii-11-11−ii1-11-1−i−iii-1-111-11ii−i−ii−i
χ13111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-1-11-11ii−i−i11iiii−i−i−i−i1-11-1−ii-11-11−i−iii-1-1111-1ii−i−i−ii
χ14111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-1-11-11ii−i−i11iiii−i−i−i−i-11-11−ii-11-11−i−iii11-1-1-11−i−iiii−i
χ15111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-1-11-11−i−iii11−i−i−i−iiiii1-11-1i−i-11-11ii−i−i-1-1111-1−i−iiii−i
χ16111-1-111-11-11-1-1111-1-111-1-1-11-1-1-1-1-11-11−i−iii11−i−i−i−iiiii-11-11i−i-11-11ii−i−i11-1-1-11ii−i−i−ii
χ1722222222222-2-222222-2-2-2222-2-2-2-200000000-2-200000000222200000000000000-2-2000000
χ1822222222222-2-222222-2-2-2222-2-2-2-200000000-2-200000000-2-2-2-20000000000000022000000
χ1922222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ23222-2-222-22-2222222-2-2-2-22-2-22222200000000-2-2000000002-22-200000000000000-22000000
χ24222-2-222-22-2222222-2-2-2-22-2-22222200000000-2-200000000-22-22000000000000002-2000000
χ25222-2-2-12-22-2-1-2-2-1-1-11122-211-111112-22-22i2i−2i−2i-1-1−i−i−i−iiiii00002i−2i-11-11−i−iii000000000000
χ26222-2-2-12-22-2-1-2-2-1-1-11122-211-111112-22-2−2i−2i2i2i-1-1iiii−i−i−i−i0000−2i2i-11-11ii−i−i000000000000
χ27222-2-2-12-22-2-1-2-2-1-1-11122-211-11111-22-222i2i−2i−2i-1-1−i−i−i−iiiii0000−2i2i1-11-1ii−i−i000000000000
χ28222-2-2-12-22-2-1-2-2-1-1-11122-211-11111-22-22−2i−2i2i2i-1-1iiii−i−i−i−i00002i−2i1-11-1−i−iii000000000000
χ2922-22-2222-2-220022-22-20002-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i222-2-20000000000000000−i2i2−i2i200
χ3022-22-2222-2-220022-22-20002-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-2-2220000000000000000i2−i2i2−i200
χ3122-22-2222-2-220022-22-20002-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i222-2-20000000000000000i2−i2i2−i200
χ3222-22-2222-2-220022-22-20002-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-2-2220000000000000000−i2i2−i2i200
χ3322-22-22-2-222222-2-2-22-22-2-2-22222-2-222-2-200002-20000000000000022-2-20000000000000000
χ3422-22-22-2-222222-2-2-22-22-2-2-22222-2-2-2-22200002-200000000000000-2-2220000000000000000
χ3522-22-22-2-2222-2-2-2-2-22-2-222-222-2-22200000000-2200000000000000000000002-22-200000000
χ3622-22-22-2-2222-2-2-2-2-22-2-222-222-2-22200000000-220000000000000000000000-22-2200000000
χ3722-22-2-1-2-222-122111-112-2-21-1-1-1-11122-2-20000-113−33−33−33−3000000-1-1113−33−3000000000000
χ3822-22-2-1-2-222-122111-112-2-21-1-1-1-11122-2-20000-11−33−33−33−33000000-1-111−33−33000000000000
χ3922-22-2-1-2-222-122111-112-2-21-1-1-1-111-2-2220000-113−33−33−33−300000011-1-1−33−33000000000000
χ4022-22-2-1-2-222-122111-112-2-21-1-1-1-111-2-2220000-11−33−33−33−3300000011-1-13−33−3000000000000
χ4122-2-2222-2-2220022-2-22000-22-2000000002−2−220022−2−2−2−2222-2-2200000000000000002−2−2200
χ4222-2-2222-2-2220022-2-22000-22-2000000002−2−220022−2−2−2−222-222-20000000000000000−222−200
χ4322-2-2222-2-2220022-2-22000-22-200000000−222−200−2−22222−2−22-2-220000000000000000−222−200
χ4422-2-2222-2-2220022-2-22000-22-200000000−222−200−2−22222−2−2-222-200000000000000002−2−2200
χ4522-2-222-222-2222-2-2-2-22-22-22-2222-2-200000000-2200000000000000000000002-2-2200000000
χ4622-2-222-222-2222-2-2-2-22-22-22-2222-2-200000000-220000000000000000000000-222-200000000
χ4722-2-222-222-22-2-2-2-2-2-222-222-22-2-2222-2-2200002-2000000000000002-2-220000000000000000
χ4822-2-222-222-22-2-2-2-2-2-222-222-22-2-222-222-200002-200000000000000-222-20000000000000000
χ4922-2-22-1-222-2-1-2-21111-12-22-11-111-1-12-2-220000-11−i3i3−i3i3i3−i3i3−i3000000-111-1−i3i3i3−i3000000000000
χ5022-2-22-1-222-2-1-2-21111-12-22-11-111-1-12-2-220000-11i3−i3i3−i3−i3i3−i3i3000000-111-1i3−i3−i3i3000000000000
χ5122-2-22-1-222-2-1-2-21111-12-22-11-111-1-1-222-20000-11−i3i3−i3i3i3−i3i3−i30000001-1-11i3−i3−i3i3000000000000
χ5222-2-22-1-222-2-1-2-21111-12-22-11-111-1-1-222-20000-11i3−i3i3−i3−i3i3−i3i30000001-1-11−i3i3i3−i3000000000000
χ53444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000000000
χ5444444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200000000220000000000000000000000000000000000
χ5544444-2-4-4-4-4-20022-2-2-200022200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5644444-2-4-4-4-4-20022-2-2-200022200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ57444-4-44-44-44400-4-44-4-400044-4000000000000000000000000000000000000000000000000
χ58444-4-4-24-44-4-244-2-2-222-4-4422-2-2-2-2-200000000220000000000000000000000000000000000
χ59444-4-4-2-44-44-20022-222000-2-22000000000000006−6−66−666−600000000000000000000000000
χ60444-4-4-2-44-44-20022-222000-2-2200000000000000−666−66−6−6600000000000000000000000000
χ6144-44-4-244-4-4-200-2-22-22000-22200000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ6244-44-4-244-4-4-200-2-22-22000-222000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6344-44-4-2-4-444-2-4-4222-22-4442-2-222-2-2000000002-20000000000000000000000000000000000
χ6444-4-44-24-4-44-200-2-222-20002-220000000022−22−222200−2−22222−2−200000000000000000000000000
χ6544-4-44-24-4-44-200-2-222-20002-2200000000−222222−220022−2−2−2−22200000000000000000000000000
χ6644-4-44-2-444-4-2442222-2-44-4-22-2-2-222000000002-20000000000000000000000000000000000
χ678-800080000-842−420000000000042−420000000000000000000000000000000000000000000000
χ688-800080000-8−424200000000000−42420000000000000000000000000000000000000000000000
χ698-8000-40000442−4243−43000000000−222226−2600000000000000000000000000000000000000000000
χ708-8000-40000442−42−4343000000000−2222−262600000000000000000000000000000000000000000000
χ718-8000-400004−424243−4300000000022−22−262600000000000000000000000000000000000000000000
χ728-8000-400004−4242−434300000000022−2226−2600000000000000000000000000000000000000000000

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