Finite Group Databasebeta

← Group #10827745

Character table — Group #10827745

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order1244222344461212224444446661212121212121244661212121212121212448812121212242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11-1111-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-1-11-1-1-1-1111111
χ7111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-11-1-1-111-1-11111
χ8111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1111-1111-1-111-1-1-1-1
χ911111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11-11-111-1-111-1-11-11-11-11-1-1-11111-1-1
χ1011111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11-11-111-1-111-1-1-11-11-11-1111-1-1-1-111
χ1111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-1111-1-111-1-11-1-111-1-111
χ1211111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-111-111-1-111-111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-1-1-111111-1111-1-1-1-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-11-1-1-11111111-1-1
χ1511111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-1-1-11111-1-111-1111-11-1-1-1-111-1-1
χ1611111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-1-1-11111-1-1-1-11-1-1-11-11111-1-111
χ172222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ192222222-1222-1-1-12222-2-2-2-2-1-1-1-11111-1-1-2-2-1-1-1-111111122-2-2-1-1-1-111110000000000000000
χ202222222-1222-1-1-12222-2-2-2-2-1-1-1-11111-1-1-2-2-1-1-1-1111111-2-2221111-1-1-1-10000000000000000
χ212222222-1222-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-21111-1-111112-22-2-1-111-1-1110000000000000000
χ222222222-1222-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-21111-1-11111-22-2211-1-111-1-10000000000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111-1-122111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111-1-122111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ252222-2-2222-2-22222-22-222-2-2-2-2222222-2-22-22-22-2-2-222-2-20000000000000000000000000000
χ262222-2-2222-2-22222-22-2-2-222-2-222-2-2-2-2-2-2-222-22-222-2-2220000000000000000000000000000
χ272222-2-2222-2-2222-22-2222-2-2-2-2222222-2-2-22-22-22-2-2-2-2220000000000000000000000000000
χ282222-2-2222-2-2222-22-22-2-222-2-222-2-2-2-2-2-22-2-22-222222-2-20000000000000000000000000000
χ292222-2-22-12-2-2-1-1-12-22-222-2-211-1-1-1-1-1-1112-2-11-1111-1-11100003−33−33−33−30000000000000000
χ302222-2-22-12-2-2-1-1-12-22-222-2-211-1-1-1-1-1-1112-2-11-1111-1-1110000−33−33−33−330000000000000000
χ312222-2-22-12-2-2-1-1-12-22-2-2-22211-1-1111111-22-11-11-1-111-1-100003−33−3−33−330000000000000000
χ322222-2-22-12-2-2-1-1-12-22-2-2-22211-1-1111111-22-11-11-1-111-1-10000−33−333−33−30000000000000000
χ332222-2-22-12-2-2-1-1-1-22-2222-2-211-1-1-1-1-1-111-221-11-11111-1-100003−3−333−3−330000000000000000
χ342222-2-22-12-2-2-1-1-1-22-2222-2-211-1-1-1-1-1-111-221-11-11111-1-10000−333−3−333−30000000000000000
χ352222-2-22-12-2-2-1-1-1-22-22-2-22211-1-11111112-21-11-1-1-1-1-11100003−3−33−333−30000000000000000
χ362222-2-22-12-2-2-1-1-1-22-22-2-22211-1-11111112-21-11-1-1-1-1-1110000−333−33−3−330000000000000000
χ3722-2-22222-2-2-22-2-22-2-220000222-20000-2-2002-2-220000000000000000002000-20002-2000000
χ3822-2-22222-2-2-22-2-22-2-220000222-20000-2-2002-2-22000000000000000000-20002000-22000000
χ3922-2-22222-2-2-22-2-2-222-20000222-20000-2-200-222-20000000000000000002000-2000-22000000
χ4022-2-22222-2-2-22-2-2-222-20000222-20000-2-200-222-2000000000000000000-200020002-2000000
χ4122-2-22-2-2222-22-2-200002i−2i2i−2i2-2-222i2i−2i−2i2-20000002i−2i0000000000000000002000-2000002i−2i00
χ4222-2-22-2-2222-22-2-200002i−2i2i−2i2-2-222i2i−2i−2i2-20000002i−2i000000000000000000-2000200000−2i2i00
χ4322-2-22-2-2222-22-2-20000−2i2i−2i2i2-2-22−2i−2i2i2i2-2000000−2i2i0000000000000000002000-200000−2i2i00
χ4422-2-22-2-2222-22-2-20000−2i2i−2i2i2-2-22−2i−2i2i2i2-2000000−2i2i000000000000000000-20002000002i−2i00
χ4522-2-2-22-222-222-2-200002i−2i−2i2i-22-222i2i−2i−2i-22000000−2i2i00000000000000000002000-20000002i−2i
χ4622-2-2-22-222-222-2-200002i−2i−2i2i-22-222i2i−2i−2i-22000000−2i2i0000000000000000000-20002000000−2i2i
χ4722-2-2-22-222-222-2-20000−2i2i2i−2i-22-22−2i−2i2i2i-220000002i−2i00000000000000000002000-2000000−2i2i
χ4822-2-2-22-222-222-2-20000−2i2i2i−2i-22-22−2i−2i2i2i-220000002i−2i0000000000000000000-200020000002i−2i
χ4922-2-2-2-222-2222-2-222-2-20000-2-22-20000220022-2-200000000000000000002000-200002-20000
χ5022-2-2-2-222-2222-2-222-2-20000-2-22-20000220022-2-20000000000000000000-200020000-220000
χ5122-2-2-2-222-2222-2-2-2-2220000-2-22-200002200-2-22200000000000000000002000-20000-220000
χ5222-2-2-2-222-2222-2-2-2-2220000-2-22-200002200-2-2220000000000000000000-2000200002-20000
χ5344444-4-44-4-44444000000004-4-4-40000-440000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-200000000-222200002-20000000023−2323−230000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-200000000-222200002-200000000−2323−23230000000000000000000000000000
χ564444-44-44-44-444400000000-44-4-400004-40000000000000000000000000000000000000000
χ574444-44-4-2-44-4-2-2-2000000002-2220000-220000000023−23−23230000000000000000000000000000
χ584444-44-4-2-44-4-2-2-2000000002-2220000-2200000000−232323−230000000000000000000000000000
χ5944-4-4444-2-4-4-4-2224-4-440000-2-2-2200002200-222-20000000000000000000000000000000000
χ6044-4-4444-2-4-4-4-222-444-40000-2-2-22000022002-2-220000000000000000000000000000000000
χ6144-4-44-4-4-244-4-22200004i−4i4i−4i-222-2−2i−2i2i2i-22000000−2i2i00000000000000000000000000000000
χ6244-4-44-4-4-244-4-2220000−4i4i−4i4i-222-22i2i−2i−2i-220000002i−2i00000000000000000000000000000000
χ6344-4-4-44-4-24-44-22200004i−4i−4i4i2-22-2−2i−2i2i2i2-20000002i−2i00000000000000000000000000000000
χ6444-4-4-44-4-24-44-2220000−4i4i4i−4i2-22-22i2i−2i−2i2-2000000−2i2i00000000000000000000000000000000
χ6544-4-4-4-44-2-444-22244-4-4000022-220000-2-200-2-2220000000000000000000000000000000000
χ6644-4-4-4-44-2-444-222-4-444000022-220000-2-20022-2-20000000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000000−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11000000000000000000000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000002ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11000000000000000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000000000000−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11000000000000000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000000002ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ11000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.