Finite Group Databasebeta

← Group #10896453

Character table — Group #10896453

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1244222344461212666888812121224242424224444881212121224242424242488884466121212121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ911111111111111111-1-1-1-1111-1-1-1-11-11-111-1-11111-1-1-1-1-1-111111-11-11-111-1-1-1-1-1-111-1-1111-1
χ1011111111111111111-1-1-1-1111-1-1-1-11-11-111-1-11111-1-1-1-1-1-1-1-1-1-11-11-11-111-1-11111-1-111-1-1-11
χ1111111111111111111-1-1-1-1111-1-1-1-11-11-1-1-111-1-1-1-11111-1-11111-111-11-1-1-111-1-11111-1-1-1-1-11
χ1211111111111111111-1-1-1-1111-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-11-1-1-11111-1-1-1-111111-1
χ1311111111111111111-1-1-1-1111-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111-11-11-11-1-111-1-1-1-1-1-11111-11
χ1411111111111111111-1-1-1-1111-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111111111-1-1-1-11-1
χ1511111111111111111-1-1-1-1111-1-1-1-1-11-11-1-111-1-1-1-11111-1-111111-1-11-1111-1-1-1-111-1-111-1-11-1
χ1611111111111111111-1-1-1-1111-1-1-1-1-11-11-1-111-1-1-1-11111-1-1-1-1-1-11-1-11-1111-1-111-1-111-1-111-11
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
χ182222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-12222-2-2-2-211111111-1-10000-2-2-1-1-1-11111000000000000
χ192222222-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
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
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-111112-22-222-2-2-1-1-1-111111100002-2-11-11-1-111000000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-111112-22-2-2-2221111-1-1-1-1110000-22-11-1111-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-11111-22-2222-2-2-1-1-1-11111110000-221-11-111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-11111-22-22-2-2221111-1-1-1-11100002-21-11-1-1-111000000000000
χ252222-2-222-22-2222-22-222-2-2-2-2222220000000000000000-2-222-2-200000000002-20000000000
χ262222-2-222-22-2222-22-222-2-2-2-2222220000000000000000-2-2-2-2220000000000-220000000000
χ272222-2-222-22-2222-22-2-2-222-2-22-2-2-2-200000000000000002222-2-20000000000-220000000000
χ282222-2-222-22-2222-22-2-2-222-2-22-2-2-2-2000000000000000022-2-22200000000002-20000000000
χ2922-2-22222-2-2-22-2-22220000-2-2-2000000002-20022-2-20000002i−2i2i−2i0000000000000000002i−2i00
χ3022-2-22222-2-2-22-2-22220000-2-2-2000000002-20022-2-2000000−2i2i−2i2i000000000000000000−2i2i00
χ3122-2-22222-2-2-22-2-22220000-2-2-200000000-2200-2-2220000002i−2i2i−2i000000000000000000−2i2i00
χ3222-2-22222-2-2-22-2-22220000-2-2-200000000-2200-2-222000000−2i2i−2i2i0000000000000000002i−2i00
χ3322-2-22-2-2222-22-2-22-2-22-22-22-2222-2-222-2-20000000000002-200000022-2-20000000000000000
χ3422-2-22-2-2222-22-2-22-2-22-22-22-2222-2-2-2-2220000000000002-2000000-2-2220000000000000000
χ3522-2-22-2-2222-22-2-22-2-2-22-222-22-2-2222-2-22000000000000-220000002-2-220000000000000000
χ3622-2-22-2-2222-22-2-22-2-2-22-222-22-2-222-222-2000000000000-22000000-222-20000000000000000
χ3722-2-22-2-2-122-2-111-1112-22-2-11-1-1-11122-2-200003−33−333−3−3-11000000-1-1113−33−3000000000000
χ3822-2-22-2-2-122-2-111-1112-22-2-11-1-1-11122-2-20000−33−33−3−333-11000000-1-111−33−33000000000000
χ3922-2-22-2-2-122-2-111-1112-22-2-11-1-1-111-2-22200003−33−333−3−3-1100000011-1-1−33−33000000000000
χ4022-2-22-2-2-122-2-111-1112-22-2-11-1-1-111-2-2220000−33−33−3−333-1100000011-1-13−33−3000000000000
χ4122-2-22-2-2-122-2-111-111-22-22-11-111-1-12-2-2200003−33−3−3−3331-1000000-111-13−3−33000000000000
χ4222-2-22-2-2-122-2-111-111-22-22-11-111-1-12-2-220000−33−3333−3−31-1000000-111-1−333−3000000000000
χ4322-2-22-2-2-122-2-111-111-22-22-11-111-1-1-222-200003−33−3−3−3331-10000001-1-11−333−3000000000000
χ4422-2-22-2-2-122-2-111-111-22-22-11-111-1-1-222-20000−33−3333−3−31-10000001-1-113−3−33000000000000
χ4522-2-2-22-22-2222-2-2-2-222-2-22-22222-2-20000000000000000-220000000000000000002i−2i2i−2i0000
χ4622-2-2-22-22-2222-2-2-2-222-2-22-22222-2-20000000000000000-22000000000000000000−2i2i−2i2i0000
χ4722-2-2-22-22-2222-2-2-2-22-222-2-222-2-22200000000000000002-20000000000000000002i−2i−2i2i0000
χ4822-2-2-22-22-2222-2-2-2-22-222-2-222-2-22200000000000000002-2000000000000000000−2i2i2i−2i0000
χ4922-2-2-2-2222-222-2-2-22-2000022-200000000002i−2i00002i−2i2i−2i002i−2i−2i2i0000000000002-200000000
χ5022-2-2-2-2222-222-2-2-22-2000022-200000000002i−2i00002i−2i2i−2i00−2i2i2i−2i000000000000-2200000000
χ5122-2-2-2-2222-222-2-2-22-2000022-20000000000−2i2i0000−2i2i−2i2i002i−2i−2i2i000000000000-2200000000
χ5222-2-2-2-2222-222-2-2-22-2000022-20000000000−2i2i0000−2i2i−2i2i00−2i2i2i−2i0000000000002-200000000
χ5344444-4-44-4-444444-4-40000-44-4000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-2-22200002-2200000000000023−23−232300000000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-2-22200002-22000000000000−232323−2300000000000000000000000000000000
χ564444-44-444-4-4444-4-4400004-4-4000000000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-2-2-222-20000-2220000000000000000−2i32i32i3−2i30000000000000000000000000000
χ584444-44-4-24-4-4-2-2-222-20000-22200000000000000002i3−2i3−2i32i30000000000000000000000000000
χ594444-4-44-2-44-4-2-2-22-2244-4-422-2-2-2-2-200000000000000002200000000000000000000000000
χ604444-4-44-2-44-4-2-2-22-22-4-44422-222220000000000000000-2-200000000000000000000000000
χ6144-4-4444-2-4-4-4-222-2-2-20000222000000004-400-2-22200000000000000000000000000000000
χ6244-4-4444-2-4-4-4-222-2-2-2000022200000000-440022-2-200000000000000000000000000000000
χ6344-4-4-44-4-2-444-22222-24-4-442-2-2-2-22200000000000000002-200000000000000000000000000
χ6444-4-4-44-4-2-444-22222-2-444-42-2-222-2-20000000000000000-2200000000000000000000000000
χ6544-4-4-4-44-24-44-2222-220000-2-2200000000004i−4i0000−2i2i−2i2i0000000000000000000000000000
χ6644-4-4-4-44-24-44-2222-220000-2-220000000000−4i4i00002i−2i2i−2i0000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i00000000002i6−2i626−2600000000000000000000000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000−2i62i6−262600000000000000000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i00000000002i6−2i6−262600000000000000000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000000−2i62i626−2600000000000000000000000000000000000000000000

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