Finite Group Databasebeta

← Group #10877350

Character table — Group #10877350

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order1244222344461212224466612121288886688888888121222448888888824242424242424242424242444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111-1-11-1
χ4111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1111111-11-1-1-1-111-1-1-1-111-1-1-1-111-11
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-11
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-11-1
χ911111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-11
χ1011111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-111-1-111-1-1111-1
χ1111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ1311111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-111111-1-1-1-1-1-111-1-1-1-1111-1
χ1411111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-111-1-111-1-111-1-1-1-111-1-1-11
χ1511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1
χ172222222-1222-1-1-12222-1-1-1-1-1-10000-1-122222222-1-1000000000022-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-12222-1-1-1-1-1-10000-1-122-2-2-2-222-1-10000000000-2-2-1-11111-1-1111100000000
χ192222222-1222-1-1-12222-1-1-1-1-1-10000-1-1-2-222-2-2-2-2-1-100000000002-211-1-11111-1-11100000000
χ202222222-1222-1-1-12222-1-1-1-1-1-10000-1-1-2-2-2-222-2-2-1-10000000000-221111-1-11111-1-100000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000112222-2-2-2-2110000000000-22-1-1-1-1111111-1-100000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-100001122-2-222-2-21100000000002-2-1-111-1-111-1-11100000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1000011-2-2222222110000000000-2-211-1-1-1-1-1-1111100000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1000011-2-2-2-2-2-22211000000000022111111-1-1-1-1-1-100000000
χ252222-2-222-2-2222200002-2-22-2-22222000000002-2002-22-2-2-20000000000002-2000000000000
χ262222-2-222-2-2222200002-2-22-2-2222200000000-2200-22-22-2-2000000000000-22000000000000
χ272222-2-222-2-2222200002-2-22-2-2-2-2-2-2000000002-200-22-22220000000000002-2000000000000
χ282222-2-222-2-2222200002-2-22-2-2-2-2-2-200000000-22002-22-222000000000000-22000000000000
χ2922-2-22222-2-2-22-2-222-2-2222-2-2-200002200000000-2-22-2-22000000000000000000002-2000000
χ3022-2-22222-2-2-22-2-222-2-2222-2-2-200002200000000-2-2-222-200000000000000000000-22000000
χ3122-2-22222-2-2-22-2-2-2-222222-2-2-20000-2-200000000222-2-2200000000000000000000-22000000
χ3222-2-22222-2-2-22-2-2-2-222222-2-2-20000-2-20000000022-222-2000000000000000000002-2000000
χ3322-2-22-2-222-222-2-20000-22-222-222-2-20000002i−2i000000002-200000000002i−2i00000000002i−2i00
χ3422-2-22-2-222-222-2-20000-22-222-222-2-2000000−2i2i000000002-20000000000−2i2i0000000000−2i2i00
χ3522-2-22-2-222-222-2-20000-22-222-2-2-2220000002i−2i00000000-2200000000002i−2i0000000000−2i2i00
χ3622-2-22-2-222-222-2-20000-22-222-2-2-222000000−2i2i00000000-220000000000−2i2i00000000002i−2i00
χ3722-2-2-22-22-2222-2-20000-2-222-2222-2-200002i−2i0000000000-22000000002i−2i00000000002i−2i0000
χ3822-2-2-22-22-2222-2-20000-2-222-2222-2-20000−2i2i0000000000-2200000000−2i2i0000000000−2i2i0000
χ3922-2-2-22-22-2222-2-20000-2-222-22-2-22200002i−2i00000000002-2000000002i−2i0000000000−2i2i0000
χ4022-2-2-22-22-2222-2-20000-2-222-22-2-2220000−2i2i00000000002-200000000−2i2i00000000002i−2i0000
χ4122-2-2-2-22222-22-2-200002-2-2-2220000002i−2i0000000022-2-2002i2i−2i−2i002i−2i000000000000000000
χ4222-2-2-2-22222-22-2-200002-2-2-2220000002i−2i00000000-2-22200−2i−2i2i2i002i−2i000000000000000000
χ4322-2-2-2-22222-22-2-200002-2-2-222000000−2i2i0000000022-2-200−2i−2i2i2i00−2i2i000000000000000000
χ4422-2-2-2-22222-22-2-200002-2-2-222000000−2i2i00000000-2-222002i2i−2i−2i00−2i2i000000000000000000
χ4544444-4-44-44-44440000-44-4-4-44000000000000000000000000000000000000000000000000
χ4644444-4-4-2-44-4-2-2-200002-2222-200000000000000000000000000000000000000−2i32i300000000
χ4744444-4-4-2-44-4-2-2-200002-2222-2000000000000000000000000000000000000002i3−2i300000000
χ484444-44-444-4-44440000-4-44-44-4000000000000000000000000000000000000000000000000
χ494444-44-4-24-4-4-2-2-2000022-22-22000000000000000000000000000000000000−2i32i30000000000
χ504444-44-4-24-4-4-2-2-2000022-22-220000000000000000000000000000000000002i3−2i30000000000
χ514444-4-44-2-4-44-2-2-20000-222-2220000000000004-400000000000000000000-22000000000000
χ524444-4-44-2-4-44-2-2-20000-222-222000000000000-44000000000000000000002-2000000000000
χ5344-4-4444-2-4-4-4-22244-4-4-2-2-22220000-2-2000000002200000000000000000000000000000000
χ5444-4-4444-2-4-4-4-222-4-444-2-2-222200002200000000-2-200000000000000000000000000000000
χ5544-4-44-4-4-24-44-22200002-22-2-2200000000004i−4i00000000000000000000−2i2i00000000000000
χ5644-4-44-4-4-24-44-22200002-22-2-220000000000−4i4i000000000000000000002i−2i00000000000000
χ5744-4-4-44-4-2-444-222000022-2-22-2000000004i−4i00000000000000000000−2i2i0000000000000000
χ5844-4-4-44-4-2-444-222000022-2-22-200000000−4i4i000000000000000000002i−2i0000000000000000
χ5944-4-4-4-44-244-4-2220000-2222-2-20000004i−4i00000000000000000000−2i2i000000000000000000
χ6044-4-4-4-44-244-4-2220000-2222-2-2000000−4i4i000000000000000000002i−2i000000000000000000
χ614-44i−4i0004000-44i−4i2-22i−2i00000022−22−2i22i22-2000000002i−2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ624-44i−4i0004000-44i−4i2-22i−2i000000−22222i2−2i22-2000000002i−2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ634-44i−4i0004000-44i−4i-22−2i2i00000022−22−2i22i2-2200000000−2i2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ644-44i−4i0004000-44i−4i-22−2i2i000000−22222i2−2i2-2200000000−2i2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ654-4−4i4i0004000-4−4i4i2-2−2i2i00000022−222i2−2i22-200000000−2i2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ664-4−4i4i0004000-4−4i4i2-2−2i2i000000−2222−2i22i22-200000000−2i2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ674-4−4i4i0004000-4−4i4i-222i−2i00000022−222i2−2i2-22000000002i−2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ684-4−4i4i0004000-4−4i4i-222i−2i000000−2222−2i22i2-22000000002i−2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ698-88i−8i000-40004−4i4i4-44i−4i0000000000-2200000000−2i2i00000000000000000000000000000000
χ708-88i−8i000-40004−4i4i-44−4i4i00000000002-2000000002i−2i00000000000000000000000000000000
χ718-8−8i8i000-400044i−4i4-4−4i4i0000000000-22000000002i−2i00000000000000000000000000000000
χ728-8−8i8i000-400044i−4i-444i−4i00000000002-200000000−2i2i00000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.