Finite Group Databasebeta

← Group #10827746

Character table — Group #10827746

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order12442223444612122244666121212222444446666661212121212121212121244446881224242424244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-111-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ411111111111111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111111111111-1-11-1-111111-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1111111-1-1
χ911111111111111-1-1-1-11111111-111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-11-1
χ1011111111111111-1-1-1-11111111-111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-11111-1-1-1-111-11
χ1111111111111111-1-1-1-11111111-1-11-1-111-1-111-1-1-1-111-1-111111111-1-11-1-1-11111-1-1-1-111-1-1-11
χ1211111111111111-1-1-1-11111111-1-11-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-111-1-11111-1-1111-1
χ1311111111111111-1-1-1-1111111-111-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-111-1-111-1-1-1-111-1-111-11
χ1411111111111111-1-1-1-1111111-111-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1111111-1-111-1-11-1
χ1511111111111111-1-1-1-1111111-11-1-11-111-1-1-1-111-1-1-1-11111111111-11-1-111-1-111-1-1-1-1-1-1111-1
χ1611111111111111-1-1-1-1111111-11-1-11-111-1-1-1-111-1-1-1-1111111-1-1-1-1-11-1-111-1-1-1-1111111-1-1-11
χ172222222-1222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-122-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-122-222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100001-2-211111000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-2-22-2-2222-1-11111-1-11111-1-1-1-10000-1-2-2-11111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111111100001221-1-1-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-12-222-22-2-211-1-11111-1-11111110000-12-2-1-1-111000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-12-2-22-2-22211-1-11111-1-111-1-1-1-100001-22111-1-1000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-222-222-2-21111-1-11111-1-111110000-1-22-111-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2-22-2221111-1-11111-1-1-1-1-1-1000012-21-1-111000000000000
χ252222-2-2222-2-22222-22-2-2-222-2-2000000002-200002-20000000022-2-200000000002-200000000
χ262222-2-2222-2-22222-22-2-2-222-2-2000000002-200002-200000000-2-2220000000000-2200000000
χ272222-2-2222-2-2222-22-22-2-222-2-200000000-220000-220000000022-2-20000000000-2200000000
χ282222-2-2222-2-2222-22-22-2-222-2-200000000-220000-2200000000-2-22200000000002-200000000
χ2922-2-22222-2-2-22-2-22-2-22222-2-2-2000000002-20000-22000000000000000000002-2002-2000000
χ3022-2-22222-2-2-22-2-22-2-22222-2-2-2000000002-20000-2200000000000000000000-2200-22000000
χ3122-2-22222-2-2-22-2-2-222-2222-2-2-200000000-2200002-2000000000000000000002-200-22000000
χ3222-2-22222-2-2-22-2-2-222-2222-2-2-200000000-2200002-200000000000000000000-22002-2000000
χ3322-2-22-2-2222-22-2-200002-2-222-20200-20000000220000-2-200002i−2i2i−2i00000000000000002i−2i00
χ3422-2-22-2-2222-22-2-200002-2-222-20200-20000000220000-2-20000−2i2i−2i2i0000000000000000−2i2i00
χ3522-2-22-2-2222-22-2-200002-2-222-20-20020000000-2-200002200002i−2i2i−2i0000000000000000−2i2i00
χ3622-2-22-2-2222-22-2-200002-2-222-20-20020000000-2-20000220000−2i2i−2i2i00000000000000002i−2i00
χ3722-2-2-22-222-222-2-20000-22-22-22200-2000000220000-2-20000002i−2i−2i2i000000000000002i−2i0000
χ3822-2-2-22-222-222-2-20000-22-22-22200-2000000220000-2-2000000−2i2i2i−2i00000000000000−2i2i0000
χ3922-2-2-22-222-222-2-20000-22-22-22-2002000000-2-20000220000002i−2i−2i2i00000000000000−2i2i0000
χ4022-2-2-22-222-222-2-20000-22-22-22-2002000000-2-2000022000000−2i2i2i−2i000000000000002i−2i0000
χ4122-2-2-2-222-2222-2-222-2-2-2-22-22200200-22-2220000-2-2000022-2-20000200-20000000000000000
χ4222-2-2-2-222-2222-2-222-2-2-2-22-22200-2002-22220000-2-20000-2-2220000-20020000000000000000
χ4322-2-2-2-222-2222-2-2-2-222-2-22-22200200-2-22-2-20000220000-2-2220000200-20000000000000000
χ4422-2-2-2-222-2222-2-2-2-222-2-22-22200-20022-2-2-2000022000022-2-20000-20020000000000000000
χ4522-2-2-2-22-1-222-11122-2-211-11-1-100200-22-2-1-1−i3i3−i3i311−i3i3−i3i3-1-1110000-1001−i3i3−i3i3000000000000
χ4622-2-2-2-22-1-222-11122-2-211-11-1-100200-22-2-1-1i3−i3i3−i311i3−i3i3−i3-1-1110000-1001i3−i3i3−i3000000000000
χ4722-2-2-2-22-1-222-11122-2-211-11-1-100-2002-22-1-1−i3i3−i3i311−i3i3−i3i311-1-10000100-1i3−i3i3−i3000000000000
χ4822-2-2-2-22-1-222-11122-2-211-11-1-100-2002-22-1-1i3−i3i3−i311i3−i3i3−i311-1-10000100-1−i3i3−i3i3000000000000
χ4922-2-2-2-22-1-222-111-2-22211-11-1-100200-2-2211−i3i3i3−i3-1-1−i3i3i3−i311-1-10000-1001−i3i3i3−i3000000000000
χ5022-2-2-2-22-1-222-111-2-22211-11-1-100200-2-2211i3−i3−i3i3-1-1i3−i3−i3i311-1-10000-1001i3−i3−i3i3000000000000
χ5122-2-2-2-22-1-222-111-2-22211-11-1-100-20022-211−i3i3i3−i3-1-1−i3i3i3−i3-1-1110000100-1i3−i3−i3i3000000000000
χ5222-2-2-2-22-1-222-111-2-22211-11-1-100-20022-211i3−i3−i3i3-1-1i3−i3−i3i3-1-1110000100-1−i3i3i3−i3000000000000
χ5344444-4-44-4-4444400004-4-4-4-44000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-20000-22222-20000000000−2i32i300002i3−2i3000000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-20000-22222-200000000002i3−2i30000−2i32i3000000000000000000000000000000
χ564444-44-44-44-44440000-44-4-44-4000000000000000000000000000000000000000000000000
χ574444-44-4-2-44-4-2-2-200002-222-22000000000000−2i32i300002i3−2i30000000000000000000000000000
χ584444-44-4-2-44-4-2-2-200002-222-220000000000002i3−2i30000−2i32i30000000000000000000000000000
χ594444-4-44-24-4-4-2-2-24-44-422-2-22200000000-220000-2200000000000000000000000000000000
χ604444-4-44-24-4-4-2-2-2-44-4422-2-222000000002-200002-200000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2224-4-44-2-2-222200000000-2200002-200000000000000000000000000000000
χ6244-4-4444-2-4-4-4-222-444-4-2-2-2222000000002-20000-2200000000000000000000000000000000
χ6344-4-44-4-4-244-4-2220000-222-2-220400-40000000-2-20000220000000000000000000000000000
χ6444-4-44-4-4-244-4-2220000-222-2-220-40040000000220000-2-20000000000000000000000000000
χ6544-4-4-44-4-24-44-22200002-22-22-2400-4000000-2-2000022000000000000000000000000000000
χ6644-4-4-44-4-24-44-22200002-22-22-2-4004000000220000-2-2000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000000000000000000000000−2i32i323−23000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000000000000000000000002i3−2i3−2323000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000000000000000000000000000000−2i32i3−2323000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000000000000000000000000002i3−2i323−23000000000000000000000000

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