Finite Group Databasebeta

← Group #10896459

Character table — Group #10896459

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order124422234446121266688881212122424242444888888121212122424242424248888882424242424242424224444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ911111111111111111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111-111-1-111-1-11-11-1-1-1-1-1111-1
χ1011111111111111111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-11-111111-1-1-11
χ1111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-111-11-11-1-1-1-111-11
χ1211111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-11-11111-1-11-1
χ1311111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1111-1-1-1-1111-11-1-1-111-1-1-11
χ1411111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-11-1111-1-1111-1
χ1511111111111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-1-1-11111-1-1-11-11-1-111-1-11-1
χ1611111111111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-11-11-111-1-111-11
χ172222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ192222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-2-2-2-2222211111111-1-10000-2-2-1-1-1-11111000000000000
χ202222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-10000221111-1-1-1-1000000000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1-1-111111100002-2-1-111-1-111000000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-11111110000-2211-1-111-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-11111-2-22222-2-21111-1-1-1-1110000-22-1-11111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-11111-2-222-2-2221111-1-1-1-11100002-211-1-1-1-111000000000000
χ252222-2-222-22-2222-2-2222-2-2-22-222220000000000000000-2-222-2-2000000000000002-2000000
χ262222-2-222-22-2222-2-2222-2-2-22-222220000000000000000-2-2-2-22200000000000000-22000000
χ272222-2-222-22-2222-2-22-2-222-22-2-2-2-2-200000000000000002222-2-200000000000000-22000000
χ282222-2-222-22-2222-2-22-2-222-22-2-2-2-2-2000000000000000022-2-222000000000000002-2000000
χ2922-2-22222-2-2-22-2-22220000-2-2-200002-200000022-2-20000002i−2i2i−2i0000000000000000002i−2i00
χ3022-2-22222-2-2-22-2-22220000-2-2-200002-200000022-2-2000000−2i2i−2i2i000000000000000000−2i2i00
χ3122-2-22222-2-2-22-2-22220000-2-2-20000-22000000-2-2220000002i−2i2i−2i000000000000000000−2i2i00
χ3222-2-22222-2-2-22-2-22220000-2-2-20000-22000000-2-222000000−2i2i−2i2i0000000000000000002i−2i00
χ3322-2-22-2-2222-22-2-22-2-22-22-222-222-2-200000000000000002-20000000000000022-2-200000000
χ3422-2-22-2-2222-22-2-22-2-22-22-222-222-2-200000000000000002-200000000000000-2-22200000000
χ3522-2-22-2-2222-22-2-22-2-2-22-2222-2-2-2220000000000000000-22000000000000002-2-2200000000
χ3622-2-22-2-2222-22-2-22-2-2-22-2222-2-2-2220000000000000000-2200000000000000-222-200000000
χ3722-2-2-22-22-2222-2-2-22-22-2-22-22222-2-200002i−2i2i−2i00000000-220000002i−2i2i−2i0000000000000000
χ3822-2-2-22-22-2222-2-2-22-22-2-22-22222-2-20000−2i2i−2i2i00000000-22000000−2i2i−2i2i0000000000000000
χ3922-2-2-22-22-2222-2-2-22-2-222-2-222-2-22200002i−2i−2i2i000000002-20000002i−2i−2i2i0000000000000000
χ4022-2-2-22-22-2222-2-2-22-2-222-2-222-2-2220000−2i2i2i−2i000000002-2000000−2i2i2i−2i0000000000000000
χ4122-2-2-22-2-1-222-1111-112-2-221-1-1-1-11100002i−2i2i−2i3−33−333−3−31-1000000−ii−ii−i3i3−i3i3000000000000
χ4222-2-2-22-2-1-222-1111-112-2-221-1-1-1-11100002i−2i2i−2i−33−33−3−3331-1000000−ii−iii3−i3i3−i3000000000000
χ4322-2-2-22-2-1-222-1111-112-2-221-1-1-1-1110000−2i2i−2i2i3−33−333−3−31-1000000i−ii−ii3−i3i3−i3000000000000
χ4422-2-2-22-2-1-222-1111-112-2-221-1-1-1-1110000−2i2i−2i2i−33−33−3−3331-1000000i−ii−i−i3i3−i3i3000000000000
χ4522-2-2-22-2-1-222-1111-11-222-21-1-111-1-100002i−2i−2i2i3−33−3−3−333-11000000−iii−i−i3i3i3−i3000000000000
χ4622-2-2-22-2-1-222-1111-11-222-21-1-111-1-100002i−2i−2i2i−33−3333−3−3-11000000−iii−ii3−i3−i3i3000000000000
χ4722-2-2-22-2-1-222-1111-11-222-21-1-111-1-10000−2i2i2i−2i3−33−3−3−333-11000000i−i−iii3−i3−i3i3000000000000
χ4822-2-2-22-2-1-222-1111-11-222-21-1-111-1-10000−2i2i2i−2i−33−3333−3−3-11000000i−i−ii−i3i3i3−i3000000000000
χ4922-2-2-2-2222-222-2-2-2-2200002-220000002i−2i000000002i−2i2i−2i002i−2i−2i2i00000000000000002-20000
χ5022-2-2-2-2222-222-2-2-2-2200002-220000002i−2i000000002i−2i2i−2i00−2i2i2i−2i0000000000000000-220000
χ5122-2-2-2-2222-222-2-2-2-2200002-22000000−2i2i00000000−2i2i−2i2i002i−2i−2i2i0000000000000000-220000
χ5222-2-2-2-2222-222-2-2-2-2200002-22000000−2i2i00000000−2i2i−2i2i00−2i2i2i−2i00000000000000002-20000
χ5344444-4-44-4-444444-4-40000-4-44000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-2-222000022-20000000000000000−2i32i32i3−2i30000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-2-222000022-200000000000000002i3−2i3−2i32i30000000000000000000000000000
χ564444-44-444-4-4444-44-400004-4-4000000000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-2-2-22-220000-22200000000000023−23−232300000000000000000000000000000000
χ584444-44-4-24-4-4-2-2-22-220000-222000000000000−232323−2300000000000000000000000000000000
χ594444-4-44-2-44-4-2-2-222-244-4-42-22-2-2-2-200000000000000002200000000000000000000000000
χ604444-4-44-2-44-4-2-2-222-2-4-4442-2222220000000000000000-2-200000000000000000000000000
χ6144-4-4444-2-4-4-4-222-2-2-2000022200004-4000000-2-22200000000000000000000000000000000
χ6244-4-4444-2-4-4-4-222-2-2-200002220000-4400000022-2-200000000000000000000000000000000
χ6344-4-44-4-4-244-4-222-2224-44-4-2-22-2-2220000000000000000-2200000000000000000000000000
χ6444-4-44-4-4-244-4-222-222-44-44-2-2222-2-200000000000000002-200000000000000000000000000
χ6544-4-4-4-44-24-44-22222-20000-22-20000004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ6644-4-4-4-44-24-44-22222-20000-22-2000000−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000026−262i6−2i600000000000000000000000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000−2626−2i62i600000000000000000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000000000026−26−2i62i600000000000000000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000000−26262i6−2i600000000000000000000000000000000000000000000

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