Finite Group Databasebeta

← Group #10827740

Character table — Group #10827740

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order1244222344461212224466612121222244444666666661212121212121212444444121212121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-111-1-1-1111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ411111111111111111111111111-111-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111111111111-1-11-1-111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ911111111111111-1-1-1-11111111-111-11-1-1-1-111-1-111-1-111-1-11111111-1-1-111-1-1-1-1-1-11111-1-11-1
χ1011111111111111-1-1-1-11111111-111-11-1-1-1-111-1-111-1-111-1-111-1-1-1-11-1-1-111-1-11111-1-1-1-111-11
χ1111111111111111-1-1-1-11111111-1-11-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1111-1-11111-1-1-1-111-1-1-11
χ1211111111111111-1-1-1-11111111-1-11-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1111-1
χ1311111111111111-1-1-1-1111111-111-111-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111-1-1-1-1111111-111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-11-1
χ1511111111111111-1-1-1-1111111-11-1-11-111-1-1-1-111-1-1-1-1-1-111-1-111111-11111-1-111-1-1-1-1-1-1111-1
χ1611111111111111-1-1-1-1111111-11-1-11-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-1111111-1-1-11
χ172222222-1222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-122-222-2-2-2-1-1-1-1-1-111-1-1-1-1-1-1110000-2-2111111000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-2-22-2-2222-1-11111-1-1-1-11111-1-10000-2-2-1-11111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111-1-111111100002211-1-1-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-12-222-22-2-211-1-111-1-111-1-111-1-100002-211-1-111000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-12-2-22-2-22211-1-1111111-1-111110000-22-1-111-1-1000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-222-222-2-21111-1-1-1-11111-1-1-1-10000-221111-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2-22-2221111-1-1111111-1-11100002-2-1-1-1-111000000000000
χ252222-2-2222-2-22222-22-22-2-22-2-2000000002-20000002-200000022-2-200000000002-200000000
χ262222-2-2222-2-22222-22-22-2-22-2-2000000002-20000002-2000000-2-2220000000000-2200000000
χ272222-2-2222-2-2222-22-222-2-22-2-200000000-22000000-2200000022-2-20000000000-2200000000
χ282222-2-2222-2-2222-22-222-2-22-2-200000000-22000000-22000000-2-22200000000002-200000000
χ2922-2-22222-2-2-22-2-22-2-22222-2-2-200200-22-22-2000022-220000-2-20000002-20000000000000000
χ3022-2-22222-2-2-22-2-22-2-22222-2-2-200-2002-222-20000-2-2-22000022000000-220000000000000000
χ3122-2-22222-2-2-22-2-2-222-2222-2-2-200200-2-22-220000222-20000-2-2000000-220000000000000000
χ3222-2-22222-2-2-22-2-2-222-2222-2-2-200-20022-2-220000-2-22-20000220000002-20000000000000000
χ3322-2-2222-1-2-2-2-1112-2-22-1-1-111100200-22-2-11−i3i3−i3i3-1-11-1−i3i3−i3i311000000-11−i3i3−i3i3000000000000
χ3422-2-2222-1-2-2-2-1112-2-22-1-1-111100200-22-2-11i3−i3i3−i3-1-11-1i3−i3i3−i311000000-11i3−i3i3−i3000000000000
χ3522-2-2222-1-2-2-2-1112-2-22-1-1-111100-2002-22-11−i3i3−i3i3111-1−i3i3−i3i3-1-10000001-1i3−i3i3−i3000000000000
χ3622-2-2222-1-2-2-2-1112-2-22-1-1-111100-2002-22-11i3−i3i3−i3111-1i3−i3i3−i3-1-10000001-1−i3i3−i3i3000000000000
χ3722-2-2222-1-2-2-2-111-222-2-1-1-111100200-2-221-1−i3i3i3−i3-1-1-11−i3i3i3−i3110000001-1−i3i3i3−i3000000000000
χ3822-2-2222-1-2-2-2-111-222-2-1-1-111100200-2-221-1i3−i3−i3i3-1-1-11i3−i3−i3i3110000001-1i3−i3−i3i3000000000000
χ3922-2-2222-1-2-2-2-111-222-2-1-1-111100-20022-21-1−i3i3i3−i311-11−i3i3i3−i3-1-1000000-11i3−i3−i3i3000000000000
χ4022-2-2222-1-2-2-2-111-222-2-1-1-111100-20022-21-1i3−i3−i3i311-11i3−i3−i3i3-1-1000000-11−i3i3i3−i3000000000000
χ4122-2-22-2-2222-22-2-20000-22-222-20200-2000000022000000-2-2002i−2i2i−2i00000000000000002i−2i00
χ4222-2-22-2-2222-22-2-20000-22-222-20200-2000000022000000-2-200−2i2i−2i2i0000000000000000−2i2i00
χ4322-2-22-2-2222-22-2-20000-22-222-20-20020000000-2-200000022002i−2i2i−2i0000000000000000−2i2i00
χ4422-2-22-2-2222-22-2-20000-22-222-20-20020000000-2-20000002200−2i2i−2i2i00000000000000002i−2i00
χ4522-2-2-22-222-222-2-20000-2-222-22200-200000022000000-2-200002i−2i−2i2i000000000000002i−2i0000
χ4622-2-2-22-222-222-2-20000-2-222-22200-200000022000000-2-20000−2i2i2i−2i00000000000000−2i2i0000
χ4722-2-2-22-222-222-2-20000-2-222-22-2002000000-2-20000002200002i−2i−2i2i00000000000000−2i2i0000
χ4822-2-2-22-222-222-2-20000-2-222-22-2002000000-2-2000000220000−2i2i2i−2i000000000000002i−2i0000
χ4922-2-2-2-222-2222-2-222-2-22-2-2-2220000000022000000-2-20000000000000000002-2002-2000000
χ5022-2-2-2-222-2222-2-222-2-22-2-2-2220000000022000000-2-2000000000000000000-2200-22000000
χ5122-2-2-2-222-2222-2-2-2-2222-2-2-22200000000-2-2000000220000000000000000002-200-22000000
χ5222-2-2-2-222-2222-2-2-2-2222-2-2-22200000000-2-200000022000000000000000000-22002-2000000
χ5344444-4-44-4-444440000-44-4-4-44000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-200002-2222-2000000000000−2i32i30000002i3−2i300000000000000000000000000
χ5544444-4-4-2-4-44-2-2-200002-2222-20000000000002i3−2i3000000−2i32i300000000000000000000000000
χ564444-44-44-44-44440000-4-44-44-4000000000000000000000000000000000000000000000000
χ574444-44-4-2-44-4-2-2-2000022-22-220000000000−2i32i30000002i3−2i30000000000000000000000000000
χ584444-44-4-2-44-4-2-2-2000022-22-2200000000002i3−2i3000000−2i32i30000000000000000000000000000
χ594444-4-44-24-4-4-2-2-24-44-4-222-22200000000-22000000-22000000000000000000000000000000
χ604444-4-44-24-4-4-2-2-2-44-44-222-222000000002-20000002-2000000000000000000000000000000
χ6144-4-44-4-4-244-4-22200002-22-2-220400-40000000-2-20000002200000000000000000000000000
χ6244-4-44-4-4-244-4-22200002-22-2-220-4004000000022000000-2-200000000000000000000000000
χ6344-4-4-44-4-24-44-222000022-2-22-2400-4000000-2-2000000220000000000000000000000000000
χ6444-4-4-44-4-24-44-222000022-2-22-2-400400000022000000-2-20000000000000000000000000000
χ6544-4-4-4-44-2-444-22244-4-4-2222-2-200000000-2-200000022000000000000000000000000000000
χ6644-4-4-4-44-2-444-222-4-444-2222-2-20000000022000000-2-2000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000000000000000000−2i32i300000023−23000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000000000000000002i3−2i3000000−2323000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000000000000000000000000−2i32i3000000−2323000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000000000000000000002i3−2i300000023−23000000000000000000000000

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