Finite Group Databasebeta

← Group #10713621

Character table — Group #10713621

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order12222344446881212666888121212242424241616161624244848484848484848448812121212242424244488161616162224
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-11
χ9111-1-1111-1-1111111-1-1-11-1-11-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−iii−i−i11-1-1
χ10111-1-1111-1-1111111-1-1-11-1-11-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−ii−ii−i−iii-1-111
χ11111-1-1111-1-1111111-1-1-11-1-11-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiii−ii−iii−i−i-1-111
χ12111-1-1111-1-1111111-1-1-11-1-11-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii−i−iii11-1-1
χ13111-1-1111-1-1111111-1-1-11-1-11-11111-1-111-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−ii−i−i−iii1-11-1
χ14111-1-1111-1-1111111-1-1-11-1-11-11111-1-111-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−ii−iiii−i−i-11-11
χ15111-1-1111-1-1111111-1-1-11-1-11-11111-1-111-1-1-1-1-1-11111−iii−i−i−iiiii−i−ii−ii−i−i−iii-11-11
χ16111-1-1111-1-1111111-1-1-11-1-11-11111-1-111-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−ii−iiii−i−i1-11-1
χ1722222222222-2-222222-2-2-2222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ1822222222222-2-222222-2-2-2222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ1922222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ23222-2-2222-2-22-2-2222-2-22-22-22-2-2-2-2-2000022000000000000000000002i−2i−2i2i00000000
χ24222-2-2222-2-22-2-2222-2-22-22-22-2-2-2-2-200002200000000000000000000−2i2i2i−2i00000000
χ25222-2-2-122-2-2-122-1-1-111-22-21-11-1-1-1-122-2-211-1-1-1-111112i−2i2i−2i−i−iii−i−iii000000000000
χ26222-2-2-122-2-2-122-1-1-111-22-21-11-1-1-1-122-2-211-1-1-1-11111−2i2i−2i2iii−i−iii−i−i000000000000
χ27222-2-2-122-2-2-122-1-1-111-22-21-11-1-1-1-1-2-222111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ28222-2-2-122-2-2-122-1-1-111-22-21-11-1-1-1-1-2-222111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ2922-22-22-222-2222-2-2-2-22-2-22-22222-2-200002-20000000000000000000000002-22-20000
χ3022-22-22-222-2222-2-2-2-22-2-22-22222-2-200002-2000000000000000000000000-22-220000
χ3122-22-22-222-22-2-2-2-2-2-2222-2-222-2-2222-22-2-2222-2-222-2-2000000000000000000000000
χ3222-22-22-222-22-2-2-2-2-2-2222-2-222-2-222-22-22-22-2-222-2-222000000000000000000000000
χ3322-22-2-1-222-2-1-2-21111-122-21-1-111-1-12-22-21-1-1-111-1-1110000−i3i3−i3i3−i3i3−i3i3000000000000
χ3422-22-2-1-222-2-1-2-21111-122-21-1-111-1-12-22-21-1-1-111-1-1110000i3−i3i3−i3i3−i3i3−i3000000000000
χ3522-22-2-1-222-2-1-2-21111-122-21-1-111-1-1-22-221-111-1-111-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ3622-22-2-1-222-2-1-2-21111-122-21-1-111-1-1-22-221-111-1-111-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ3722-2-222-22-22222-2-2-22-22-2-222-222-2-20000-220000000000000000000000002i−2i−2i2i0000
χ3822-2-222-22-22222-2-2-22-22-2-222-222-2-20000-22000000000000000000000000−2i2i2i−2i0000
χ3922-2-222-22-222-2-2-2-2-22-2-22222-2-2-2222-2-222-222-2-2-2-222000000000000000000000000
χ4022-2-222-22-222-2-2-2-2-22-2-22222-2-2-222-222-22-2-2-22222-2-2000000000000000000000000
χ4122-2-22-1-22-22-1-2-2111-11-222-1-1111-1-12-2-22-11-1-11111-1-100003−3−333−3−33000000000000
χ4222-2-22-1-22-22-1-2-2111-11-222-1-1111-1-12-2-22-11-1-11111-1-10000−333−3−333−3000000000000
χ4322-2-22-1-22-22-1-2-2111-11-222-1-1111-1-1-222-2-1111-1-1-1-11100003−3−33−333−3000000000000
χ4422-2-22-1-22-22-1-2-2111-11-222-1-1111-1-1-222-2-1111-1-1-1-1110000−333−33−3−33000000000000
χ45444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000
χ4644444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200002200000000000000000000000000000000
χ4744444-2-4-4-4-4-20022-2-2-200022200000000006−66−66−66−6000000000000000000000000
χ4844444-2-4-4-4-4-20022-2-2-20002220000000000−66−66−66−66000000000000000000000000
χ49444-4-44-4-444400-4-44-4-40004-44000000000000000000000000000000000000000000
χ50444-4-4-244-4-4-2-4-4-2-2-2224-442-2222220000-2-200000000000000000000000000000000
χ51444-4-4-2-4-444-20022-222000-22-200000000006−66−6−66−66000000000000000000000000
χ52444-4-4-2-4-444-20022-222000-22-20000000000−66−666−66−6000000000000000000000000
χ5344-44-444-4-4440044-4-440004-4-4000000000000000000000000000000000000000000
χ5444-44-4-24-4-44-200-2-222-2000-22200000000006−6−666−6−66000000000000000000000000
χ5544-44-4-24-4-44-200-2-222-2000-2220000000000−666−6−666−6000000000000000000000000
χ5644-44-4-2-444-4-2442222-2-4-442-2-2-2-2220000-2200000000000000000000000000000000
χ5744-4-4444-44-440044-44-4000-4-44000000000000000000000000000000000000000000
χ5844-4-44-24-44-4-200-2-22-2200022-200000000006−6−66−666−6000000000000000000000000
χ5944-4-44-24-44-4-200-2-22-2200022-20000000000−666−66−6−66000000000000000000000000
χ6044-4-44-2-44-44-244222-224-4-4-2-22-2-22200002-200000000000000000000000000000000
χ618-800080000-842−420000000000042−420000000000000000000000000000000000000000
χ628-800080000-8−424200000000000−42420000000000000000000000000000000000000000
χ638-8000-40000442−4243−43000000000−222226−2600000000000000000000000000000000000000
χ648-8000-40000442−42−4343000000000−2222−262600000000000000000000000000000000000000
χ658-8000-400004−424243−4300000000022−22−262600000000000000000000000000000000000000
χ668-8000-400004−4242−434300000000022−2226−2600000000000000000000000000000000000000

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