Finite Group Databasebeta

← Group #10831100

Character table — Group #10831100

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order1244222344461212222244446661212128888224444666666661212121212121212888888441212121212122244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ51111111111111111-1-111-1-111111111111111-1-111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-111-1-1111111-1-1-1-11111-1-111-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1
χ911111111111111-1-111-1-11111111111111-11-1-1-1-1-11111-1-1-1-11111-1-11111111-1-1-111-1-11-11-1-1-1-1-11-1
χ1011111111111111-1-111-1-1111111111111-11-11-1-1-1-111-1-111-1-111-1-111111111-11-1-1-1-111-11-11-1-1-1-1-11
χ1111111111111111-1-111-1-111111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-111-1-1-11-111111-11
χ1211111111111111-1-111-1-111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-11-1-1-1-1111-11-111111-1
χ1311111111111111-1-1-1-1-1-1-1-111111111111-11-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-1111-11-111-1-1-11
χ1411111111111111-1-1-1-1-1-1-1-11111111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11111-1-1-11-1111-1-11-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1111-1-111-11-11-1-1111-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-1-1-111-1-1-1-1-1-111-1-111111-11111-1-11-11-1-1-111-11
χ172222222-1222-1-1-122222222-1-1-1-1-1-10000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-10000-2-2-2-222-1-1-1-11111-1-1-1-11111000000-2-2-1-111110000000000
χ192222222-1222-1-1-122-2-222-2-2-1-1-1-1-1-100002222-2-2-1-111-1-1-1-1-1-111-1-1-1-1000000-2-21111110000000000
χ202222222-1222-1-1-122-2-222-2-2-1-1-1-1-1-10000-2-2-2-2-2-2-1-1111111-1-11111110000002211-1-1-1-10000000000
χ212222222-1222-1-1-1-2-222-2-222-1-1-1-1-1-100002-22-2-2-211-1-1-1-11111-1-1-1-1110000002-211-1-1110000000000
χ222222222-1222-1-1-1-2-222-2-222-1-1-1-1-1-10000-22-22-2-211-1-111-1-111-1-111-1-1000000-221111-1-10000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100002-22-2221111-1-1111111-1-111000000-22-1-111-1-10000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-10000-22-2222111111-1-1111111-1-10000002-2-1-1-1-1110000000000
χ2522222-2-22-2-222222-2002-2002-2-22-2-222220000002-20000002-2000000-2-20000000000000000002-200
χ2622222-2-22-2-222222-2002-2002-2-22-2-2-2-2-2-20000002-20000002-200000022000000000000000000-2200
χ2722222-2-22-2-22222-2200-22002-2-22-2-22222000000-22000000-22000000-2-2000000000000000000-2200
χ2822222-2-22-2-22222-2200-22002-2-22-2-2-2-2-2-2000000-22000000-22000000220000000000000000002-200
χ2922-2-22222-2-2-22-2-22-222-22-2-2222-2-2-2000000002-22-2220000-22-2-20000000000002-200000000000000
χ3022-2-22222-2-2-22-2-22-2-2-2-2222222-2-2-200000000-222-2-2-20000-2222000000000000-2200000000000000
χ3122-2-22222-2-2-22-2-2-22222-2-2-2222-2-2-200000000-22-222200002-2-2-2000000000000-2200000000000000
χ3222-2-22222-2-2-22-2-2-22-2-22-222222-2-2-2000000002-2-22-2-200002-2220000000000002-200000000000000
χ3322-2-2222-1-2-2-2-1112-222-22-2-2-1-1-1111000000002-2-11-1-1−i3i3−i3i31-111−i3i3−i3i300000000-11−i3i3−i3i30000000000
χ3422-2-2222-1-2-2-2-1112-222-22-2-2-1-1-1111000000002-2-11-1-1i3−i3i3−i31-111i3−i3i3−i300000000-11i3−i3i3−i30000000000
χ3522-2-2222-1-2-2-2-1112-2-2-2-2222-1-1-111100000000-22-1111−i3i3−i3i31-1-1-1−i3i3−i3i3000000001-1i3−i3i3−i30000000000
χ3622-2-2222-1-2-2-2-1112-2-2-2-2222-1-1-111100000000-22-1111i3−i3i3−i31-1-1-1i3−i3i3−i3000000001-1−i3i3−i3i30000000000
χ3722-2-2222-1-2-2-2-111-22222-2-2-2-1-1-111100000000-221-1-1-1−i3i3i3−i3-1111−i3i3i3−i3000000001-1−i3i3i3−i30000000000
χ3822-2-2222-1-2-2-2-111-22222-2-2-2-1-1-111100000000-221-1-1-1i3−i3−i3i3-1111i3−i3−i3i3000000001-1i3−i3−i3i30000000000
χ3922-2-2222-1-2-2-2-111-22-2-22-222-1-1-1111000000002-21-111−i3i3i3−i3-11-1-1−i3i3i3−i300000000-11i3−i3−i3i30000000000
χ4022-2-2222-1-2-2-2-111-22-2-22-222-1-1-1111000000002-21-111i3−i3−i3i3-11-1-1i3−i3−i3i300000000-11−i3i3i3−i30000000000
χ4122-2-22-2-2222-22-2-22200-2-2002-2-2-222000000000022000000-2-2000000002i2i−2i−2i0000000000002i−2i0000
χ4222-2-22-2-2222-22-2-22200-2-2002-2-2-222000000000022000000-2-200000000−2i−2i2i2i000000000000−2i2i0000
χ4322-2-22-2-2222-22-2-2-2-20022002-2-2-2220000000000-2-200000022000000002i2i−2i−2i000000000000−2i2i0000
χ4422-2-22-2-2222-22-2-2-2-20022002-2-2-2220000000000-2-20000002200000000−2i−2i2i2i0000000000002i−2i0000
χ4522-2-2-22-222-222-2-200000000-22-222-222-2-2020-20000000022000000-2-22-2000000000000020-2000000
χ4622-2-2-22-222-222-2-200000000-22-222-222-2-20-20200000000-2-2000000222-20000000000000-202000000
χ4722-2-2-22-222-222-2-200000000-22-222-2-2-222020-20000000022000000-2-2-220000000000000-202000000
χ4822-2-2-22-222-222-2-200000000-22-222-2-2-2220-20200000000-2-200000022-22000000000000020-2000000
χ4922-2-2-2-222-2222-2-200000000-2-222-2222-2-220-2000000022000000-2-200-2200000000000020-20000000
χ5022-2-2-2-222-2222-2-200000000-2-222-2222-2-2-2020000000-2-20000002200-22000000000000-2020000000
χ5122-2-2-2-222-2222-2-200000000-2-222-22-2-22220-2000000022000000-2-2002-2000000000000-2020000000
χ5222-2-2-2-222-2222-2-200000000-2-222-22-2-222-2020000000-2-200000022002-200000000000020-20000000
χ5344444-4-4-2-4-44-2-2-24-4004-400-222-2220000000000-22000000-22000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-2-4400-4400-222-22200000000002-20000002-2000000000000000000000000000000
χ554444-44-44-44-444400000000-44-4-4-4400000000000000000000000000000000000000000000000000
χ564444-44-4-2-44-4-2-2-2000000002-2222-20000000000000000−2i32i30000002i3−2i3000000000000000000000000
χ574444-44-4-2-44-4-2-2-2000000002-2222-200000000000000002i3−2i3000000−2i32i3000000000000000000000000
χ584444-4-4444-4-444400000000-4-44-44-400000000000000000000000000000000000000000000000000
χ594444-4-44-24-4-4-2-2-20000000022-22-2200000000000000−2i32i30000002i3−2i300000000000000000000000000
χ604444-4-44-24-4-4-2-2-20000000022-22-22000000000000002i3−2i3000000−2i32i300000000000000000000000000
χ6144-4-44-4-4-244-4-2224400-4-400-2222-2-20000000000-2-200000022000000000000000000000000000000
χ6244-4-44-4-4-244-4-222-4-4004400-2222-2-2000000000022000000-2-2000000000000000000000000000000
χ6344-4-4-44-4-24-44-222000000002-22-2-220000040-400000000-2-200000022000000000000000000000000
χ6444-4-4-44-4-24-44-222000000002-22-2-2200000-4040000000022000000-2-2000000000000000000000000
χ6544-4-4-4-44-2-444-2220000000022-2-22-2000040-40000000-2-20000002200000000000000000000000000
χ6644-4-4-4-44-2-444-2220000000022-2-22-20000-404000000022000000-2-200000000000000000000000000
χ674-44i−4i0004000-44i−4i002-2002i−2i00000022−22−2i22i2000000002-20000002i−2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ684-44i−4i0004000-44i−4i002-2002i−2i000000−22222i2−2i2000000002-20000002i−2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ694-44i−4i0004000-44i−4i00-2200−2i2i00000022−22−2i22i200000000-22000000−2i2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ704-44i−4i0004000-44i−4i00-2200−2i2i000000−22222i2−2i200000000-22000000−2i2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ714-4−4i4i0004000-4−4i4i002-200−2i2i00000022−222i2−2i2000000002-2000000−2i2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ724-4−4i4i0004000-4−4i4i002-200−2i2i000000−2222−2i22i2000000002-2000000−2i2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ734-4−4i4i0004000-4−4i4i00-22002i−2i00000022−222i2−2i200000000-220000002i−2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ744-4−4i4i0004000-4−4i4i00-22002i−2i000000−2222−2i22i200000000-220000002i−2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ758-88i−8i000-40004−4i4i004-4004i−4i000000000000000000-22000000−2i2i0000000000000000000000000000
χ768-88i−8i000-40004−4i4i00-4400−4i4i0000000000000000002-20000002i−2i0000000000000000000000000000
χ778-8−8i8i000-400044i−4i004-400−4i4i000000000000000000-220000002i−2i0000000000000000000000000000
χ788-8−8i8i000-400044i−4i00-44004i−4i0000000000000000002-2000000−2i2i0000000000000000000000000000

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