Finite Group Databasebeta

← Group #10896454

Character table — Group #10896454

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order1244222344461212666888812121224446688881212242424242424242424242424888848121212122424244444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ911111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-111-1-1-1-1-1-1111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111111-1-1-11
χ1111111111111111111-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-111-1-1-1-1-11
χ1211111111111111111-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111-1-111111-1
χ1311111111111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-1-1-1-11111-11
χ1411111111111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-11-1
χ1511111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-111-1-1-1-1-1-11111-1-11-1
χ1611111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-11111-1-1-1-111-11
χ172222222-1222-1-1-1-1-1-12222-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-12222-1-1-122-2-2-1-122-2-2-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ192222222-1222-1-1-1-1-1-12222-1-1-1-2-22211-2-22211-1-1-1-11111-1-1-1-10000-2-2-1-11111000000000000
χ202222222-1222-1-1-1-1-1-12222-1-1-1-2-2-2-211-2-2-2-211-1-1-1-11111111100002211-1-1-1-1000000000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-12222-1-1-2-2-2-2-1-111111111111100002-2-1-1-1-111000000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-122-2-2-1-1-2-222-1-111111111-1-1-1-10000-221111-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-2221122-2-2111111-1-1-1-111110000-22-1-111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-2-2-2112222111111-1-1-1-1-1-1-1-100002-211-1-111000000000000
χ252222-2-222-22-2222-22-222-2-22-2-200000000000022-2-20000000022-2-200000000002-200000000
χ262222-2-222-22-2222-22-222-2-22-2-200000000000022-2-200000000-2-2220000000000-2200000000
χ272222-2-222-22-2222-22-2-2-2222-2-2000000000000-2-2220000000022-2-20000000000-2200000000
χ282222-2-222-22-2222-22-2-2-2222-2-2000000000000-2-22200000000-2-22200000000002-200000000
χ2922-2-22222-2-2-22-2-22222i−2i2i−2i-2-2-2002-200002i−2i002i−2i2i−2i00002i2i−2i−2i0000002-20000000000000000
χ3022-2-22222-2-2-22-2-22222i−2i2i−2i-2-2-200-220000−2i2i002i−2i2i−2i0000−2i−2i2i2i000000-220000000000000000
χ3122-2-22222-2-2-22-2-2222−2i2i−2i2i-2-2-2002-20000−2i2i00−2i2i−2i2i0000−2i−2i2i2i0000002-20000000000000000
χ3222-2-22222-2-2-22-2-2222−2i2i−2i2i-2-2-200-2200002i−2i00−2i2i−2i2i00002i2i−2i−2i000000-220000000000000000
χ3322-2-2222-1-2-2-2-111-1-1-12i−2i2i−2i111002-2−i3i3002i−2i−i3i3−ii−ii33−3−3−i−iii000000-11−i3i33−3000000000000
χ3422-2-2222-1-2-2-2-111-1-1-12i−2i2i−2i111002-2i3−i3002i−2ii3−i3−ii−ii−3−333−i−iii000000-11i3−i3−33000000000000
χ3522-2-2222-1-2-2-2-111-1-1-12i−2i2i−2i11100-22−i3i300−2i2i−i3i3−ii−ii33−3−3ii−i−i0000001-1i3−i3−33000000000000
χ3622-2-2222-1-2-2-2-111-1-1-12i−2i2i−2i11100-22i3−i300−2i2ii3−i3−ii−ii−3−333ii−i−i0000001-1−i3i33−3000000000000
χ3722-2-2222-1-2-2-2-111-1-1-1−2i2i−2i2i111002-2−i3i300−2i2i−i3i3i−ii−i−3−333ii−i−i000000-11−i3i3−33000000000000
χ3822-2-2222-1-2-2-2-111-1-1-1−2i2i−2i2i111002-2i3−i300−2i2ii3−i3i−ii−i33−3−3ii−i−i000000-11i3−i33−3000000000000
χ3922-2-2222-1-2-2-2-111-1-1-1−2i2i−2i2i11100-22−i3i3002i−2i−i3i3i−ii−i−3−333−i−iii0000001-1i3−i33−3000000000000
χ4022-2-2222-1-2-2-2-111-1-1-1−2i2i−2i2i11100-22i3−i3002i−2ii3−i3i−ii−i33−3−3−i−iii0000001-1−i3i3−33000000000000
χ4122-2-22-2-2222-22-2-22-2-2000022-22-200220000-2-20000000000002-22-2000000002-20000000000
χ4222-2-22-2-2222-22-2-22-2-2000022-22-200220000-2-2000000000000-22-2200000000-220000000000
χ4322-2-22-2-2222-22-2-22-2-2000022-2-2200-2-20000220000000000002-22-200000000-220000000000
χ4422-2-22-2-2222-22-2-22-2-2000022-2-2200-2-2000022000000000000-22-22000000002-20000000000
χ4522-2-2-22-22-2222-2-2-2-2200002-220000002i−2i000000002i−2i2i−2i00002-2-22000000000000002i−2i0000
χ4622-2-2-22-22-2222-2-2-2-2200002-220000002i−2i000000002i−2i2i−2i0000-222-200000000000000−2i2i0000
χ4722-2-2-22-22-2222-2-2-2-2200002-22000000−2i2i00000000−2i2i−2i2i00002-2-2200000000000000−2i2i0000
χ4822-2-2-22-22-2222-2-2-2-2200002-22000000−2i2i00000000−2i2i−2i2i0000-222-2000000000000002i−2i0000
χ4922-2-2-2-2222-222-2-2-22-22i−2i−2i2i-2220000000000002i−2i−2i2i0000000000000000000000002-2002i−2i00
χ5022-2-2-2-2222-222-2-2-22-22i−2i−2i2i-2220000000000002i−2i−2i2i000000000000000000000000-2200−2i2i00
χ5122-2-2-2-2222-222-2-2-22-2−2i2i2i−2i-222000000000000−2i2i2i−2i0000000000000000000000002-200−2i2i00
χ5222-2-2-2-2222-222-2-2-22-2−2i2i2i−2i-222000000000000−2i2i2i−2i000000000000000000000000-22002i−2i00
χ5344444-4-44-4-444444-4-40000-4-44000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-2-222000022-20000−2i32i300002i3−2i3000000000000000000000000000000000000
χ5544444-4-4-2-4-44-2-2-2-222000022-200002i3−2i30000−2i32i3000000000000000000000000000000000000
χ564444-44-444-4-4444-4-440000-44-4000000000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-2-2-222-200002-220000000000000000−2i32i32i3−2i30000000000000000000000000000
χ584444-44-4-24-4-4-2-2-222-200002-2200000000000000002i3−2i3−2i32i30000000000000000000000000000
χ594444-4-44-2-44-4-2-2-22-2244-4-4-222000000000000-2-22200000000000000000000000000000000
χ604444-4-44-2-44-4-2-2-22-22-4-444-22200000000000022-2-200000000000000000000000000000000
χ6144-4-44-4-4-244-4-222-2220000-2-224-400-2-2000022000000000000000000000000000000000000
χ6244-4-44-4-4-244-4-222-2220000-2-22-4400220000-2-2000000000000000000000000000000000000
χ6344-4-4-44-4-2-444-22222-20000-22-20000004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ6444-4-4-44-4-2-444-22222-20000-22-2000000−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ6544-4-4-4-44-24-44-2222-224i−4i−4i4i2-2-2000000000000−2i2i2i−2i00000000000000000000000000000000
χ6644-4-4-4-44-24-44-2222-22−4i4i4i−4i2-2-20000000000002i−2i−2i2i00000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000000000000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000000000000000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i0000000000000000000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000
χ728-8−8i8i000-400044i−4i000000000000000000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000

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