Finite Group Databasebeta

← Group #10827748

Character table — Group #10827748

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order124422234446121222446661212122444668888121212121212242424242424242444444461212121212222444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ911111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-11-1-11-1-1-1111-1
χ1011111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-11-111-1111-1-1-11
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-11-1-11-1-111-11
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-11111-111-111-1-11-1
χ1311111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-11-1-1-1-11111-111-1-1-1-1-1-11
χ1411111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1111111-1
χ1511111111111111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-111-1-11-111-11-1-1-1-11-1
χ1611111111111111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-1-11-1-11-11111-11
χ172222222-1222-1-1-12222-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-2-1-11111000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-12222-1-11111-1-1-1-1-1-1-1-10000-2-2111111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111111111111100002211-1-1-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-21122-2-2111111-1-1-1-1111100002-2-1-1-1-111000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-211-2-2221111111111-1-1-1-10000-22-1-111-1-1000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2221122-2-211-1-1-1-1-1-1-1-111110000-221111-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22211-2-22211-1-1-1-11111-1-1-1-100002-211-1-111000000000000
χ252222-2-2222-2-22222-22-22-2-22-2-200002-200002-200000000000022-2-2000000000000002-20000
χ262222-2-2222-2-22222-22-22-2-22-2-200002-200002-2000000000000-2-22200000000000000-220000
χ272222-2-2222-2-2222-22-222-2-22-2-20000-220000-2200000000000022-2-200000000000000-220000
χ282222-2-2222-2-2222-22-222-2-22-2-20000-220000-22000000000000-2-222000000000000002-20000
χ2922-2-22222-2-2-22-2-22-2-22222-2-2-200002-20000-22000000000000000000000000200-200002-200
χ3022-2-22222-2-2-22-2-22-2-22222-2-2-200002-20000-22000000000000000000000000-20020000-2200
χ3122-2-22222-2-2-22-2-2-222-2222-2-2-20000-2200002-2000000000000000000000000200-20000-2200
χ3222-2-22222-2-2-22-2-2-222-2222-2-2-20000-2200002-2000000000000000000000000-200200002-200
χ3322-2-22-2-2222-22-2-20000-22-222-2000000002i−2i00000000002i2i−2i−2i2i−2i2i−2i0000000000200-2000000
χ3422-2-22-2-2222-22-2-20000-22-222-2000000002i−2i00000000002i2i−2i−2i−2i2i−2i2i0000000000-2002000000
χ3522-2-22-2-2222-22-2-20000-22-222-200000000−2i2i0000000000−2i−2i2i2i2i−2i2i−2i0000000000-2002000000
χ3622-2-22-2-2222-22-2-20000-22-222-200000000−2i2i0000000000−2i−2i2i2i−2i2i−2i2i0000000000200-2000000
χ3722-2-2-22-222-222-2-20000-2-222-220000002i−2i000000002i2i−2i−2i00002i−2i−2i2i000000000200-20000000
χ3822-2-2-22-222-222-2-20000-2-222-220000002i−2i000000002i2i−2i−2i0000−2i2i2i−2i000000000-20020000000
χ3922-2-2-22-222-222-2-20000-2-222-22000000−2i2i00000000−2i−2i2i2i00002i−2i−2i2i000000000-20020000000
χ4022-2-2-22-222-222-2-20000-2-222-22000000−2i2i00000000−2i−2i2i2i0000−2i2i2i−2i000000000200-20000000
χ4122-2-2-2-222-2222-2-222-2-22-2-2-2222-22-2220000-2-222-2-2000000000000002-20000000000000000
χ4222-2-2-2-222-2222-2-222-2-22-2-2-222-22-22220000-2-2-2-22200000000000000-220000000000000000
χ4322-2-2-2-222-2222-2-2-2-2222-2-2-2222-2-22-2-2000022-2-222000000000000002-20000000000000000
χ4422-2-2-2-222-2222-2-2-2-2222-2-2-222-222-2-2-200002222-2-200000000000000-220000000000000000
χ4522-2-2-2-22-1-222-11122-2-2-1111-1-12-22-2-1-1000011-1-1113−33−33−33−3000000-113−33−3000000000000
χ4622-2-2-2-22-1-222-11122-2-2-1111-1-12-22-2-1-1000011-1-111−33−33−33−33000000-11−33−33000000000000
χ4722-2-2-2-22-1-222-11122-2-2-1111-1-1-22-22-1-100001111-1-13−33−33−33−30000001-1−33−33000000000000
χ4822-2-2-2-22-1-222-11122-2-2-1111-1-1-22-22-1-100001111-1-1−33−33−33−330000001-13−33−3000000000000
χ4922-2-2-2-22-1-222-111-2-222-1111-1-12-2-22110000-1-111-1-13−33−3−33−33000000-113−3−33000000000000
χ5022-2-2-2-22-1-222-111-2-222-1111-1-12-2-22110000-1-111-1-1−33−333−33−3000000-11−333−3000000000000
χ5122-2-2-2-22-1-222-111-2-222-1111-1-1-222-2110000-1-1-1-1113−33−3−33−330000001-1−333−3000000000000
χ5222-2-2-2-22-1-222-111-2-222-1111-1-1-222-2110000-1-1-1-111−33−333−33−30000001-13−3−33000000000000
χ5344444-4-44-4-444440000-44-4-4-44000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-200002-2222-20000000000000000−2i32i32i3−2i30000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-200002-2222-200000000000000002i3−2i3−2i32i30000000000000000000000000000
χ564444-44-44-44-44440000-4-44-44-4000000000000000000000000000000000000000000000000
χ574444-44-4-2-44-4-2-2-2000022-22-2200000000000000000000−2i32i32i3−2i3000000000000000000000000
χ584444-44-4-2-44-4-2-2-2000022-22-22000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ594444-4-44-24-4-4-2-2-24-44-4-222-2220000-220000-22000000000000000000000000000000000000
χ604444-4-44-24-4-4-2-2-2-44-44-222-22200002-200002-2000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2224-4-44-2-2-22220000-2200002-2000000000000000000000000000000000000
χ6244-4-4444-2-4-4-4-222-444-4-2-2-222200002-20000-22000000000000000000000000000000000000
χ6344-4-44-4-4-244-4-22200002-22-2-22000000004i−4i0000000000−2i−2i2i2i000000000000000000000000
χ6444-4-44-4-4-244-4-22200002-22-2-2200000000−4i4i00000000002i2i−2i−2i000000000000000000000000
χ6544-4-4-44-4-24-44-222000022-2-22-20000004i−4i00000000−2i−2i2i2i0000000000000000000000000000
χ6644-4-4-44-4-24-44-222000022-2-22-2000000−4i4i000000002i2i−2i−2i0000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i0000000000000000000000−2i32i323−2300000000000000000000000000000000
χ698-88i−8i000-40004−4i4i00000000000000000000002i3−2i3−232300000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i0000000000000000000000−2i32i3−232300000000000000000000000000000000
χ728-8−8i8i000-400044i−4i00000000000000000000002i3−2i323−2300000000000000000000000000000000

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