Finite Group Databasebeta

← Group #10896445

Character table — Group #10896445

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order1244222344461212444466688881212128888246688881212121212122424242424242424888888481212242424242444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-1-1-1-1-1-11
χ6111111111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-111111111111-111-1-1-1-1-1-1-1-1-1-1111-1
χ7111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-1
χ8111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-1111111-1-1-11
χ911111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1
χ1011111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-11111-1-1
χ1311111111111111-1-1-1-1111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-111-1-111-1-11-1
χ1411111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-1-11111-1-1-1-11111-11
χ1511111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11111-1-1-1-111-1-111-11
χ1611111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-111111111-1-1-1-11-1
χ172222222-1222-1-1-12222-1-1-12222-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ182222222-1222-1-1-12222-1-1-12222-1-1-10000-2-21122-2-211-1-1-1-1-1-1-1-11111000000-2-211-1-1110000000000
χ192222222-1222-1-1-12222-1-1-1-2-2-2-2-1-1-1000022-1-1-2-2-2-2-1-1-1-1-1-111111111000000-221111-1-10000000000
χ202222222-1222-1-1-12222-1-1-1-2-2-2-2-1-1-10000-2-211-2-22211-1-1-1-11111-1-1-1-10000002-2-1-111110000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-12222-1-1-1000022-1-1-2-222-1-11111-1-1-1-1-1-1-1-1000000-2-21111110000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-12222-1-1-10000-2-211-2-2-2-2111111-1-1-1-1111100000022-1-111-1-10000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-2-1-1-1000022-1-122-2-2-1-11111111111110000002-2-1-1-1-1110000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-2-1-1-10000-2-21122221111111111-1-1-1-1000000-2211-1-1-1-10000000000
χ252222-2-222-22-22220000-22-222-2-22-2-222220000000000000022-2-200000000-2-200000000002-2000000
χ262222-2-222-22-22220000-22-222-2-22-2-2-2-2-2-20000000000000022-2-200000000220000000000-22000000
χ272222-2-222-22-22220000-22-2-2-2222-2-2222200000000000000-2-22200000000-2-20000000000-22000000
χ282222-2-222-22-22220000-22-2-2-2222-2-2-2-2-2-200000000000000-2-222000000002200000000002-2000000
χ2922-2-22222-2-2-22-2-200002222i−2i2i−2i-2-2-20000000000000000002i−2i2i−2i00002i2i−2i−2i000000000000002-20000
χ3022-2-22222-2-2-22-2-200002222i−2i2i−2i-2-2-20000000000000000002i−2i2i−2i0000−2i−2i2i2i00000000000000-220000
χ3122-2-22222-2-2-22-2-20000222−2i2i−2i2i-2-2-2000000000000000000−2i2i−2i2i00002i2i−2i−2i00000000000000-220000
χ3222-2-22222-2-2-22-2-20000222−2i2i−2i2i-2-2-2000000000000000000−2i2i−2i2i0000−2i−2i2i2i000000000000002-20000
χ3322-2-22-2-2222-22-2-200002-2-2000022-222-2-22-2220000-2-200000000000000002-2000000002-200000000
χ3422-2-22-2-2222-22-2-200002-2-2000022-222-2-2-22-2-200002200000000000000002-200000000-2200000000
χ3522-2-22-2-2222-22-2-200002-2-2000022-2-2-2222-2220000-2-20000000000000000-2200000000-2200000000
χ3622-2-22-2-2222-22-2-200002-2-2000022-2-2-222-22-2-20000220000000000000000-22000000002-200000000
χ3722-2-2-22-22-2222-2-20000-2-2200002-2222-2-20000002i−2i00000000002i2i−2i−2i0000-22000000000000002i−2i00
χ3822-2-2-22-22-2222-2-20000-2-2200002-2222-2-2000000−2i2i0000000000−2i−2i2i2i0000-2200000000000000−2i2i00
χ3922-2-2-22-22-2222-2-20000-2-2200002-22-2-2220000002i−2i00000000002i2i−2i−2i00002-200000000000000−2i2i00
χ4022-2-2-22-22-2222-2-20000-2-2200002-22-2-222000000−2i2i0000000000−2i−2i2i2i00002-2000000000000002i−2i00
χ4122-2-2-2-2222-222-2-222-2-2-22-22i−2i−2i2i-222000000002i−2i000022-2-22i−2i−2i2i000000000000002i−2i000000000000
χ4222-2-2-2-2222-222-2-222-2-2-22-2−2i2i2i−2i-22200000000−2i2i000022-2-2−2i2i2i−2i00000000000000−2i2i000000000000
χ4322-2-2-2-2222-222-2-2-2-222-22-22i−2i−2i2i-22200000000−2i2i0000-2-2222i−2i−2i2i00000000000000−2i2i000000000000
χ4422-2-2-2-2222-222-2-2-2-222-22-2−2i2i2i−2i-222000000002i−2i0000-2-222−2i2i2i−2i000000000000002i−2i000000000000
χ4522-2-2-2-22-12-22-11122-2-21-112i−2i−2i2i1-1-1000000−i3i32i−2i00−i3i3-1-111−iii−i3−33−3000000003−3−ii−i3i30000000000
χ4622-2-2-2-22-12-22-11122-2-21-112i−2i−2i2i1-1-1000000i3−i32i−2i00i3−i3-1-111−iii−i−33−3300000000−33−iii3−i30000000000
χ4722-2-2-2-22-12-22-11122-2-21-11−2i2i2i−2i1-1-1000000−i3i3−2i2i00−i3i3-1-111i−i−ii−33−3300000000−33i−i−i3i30000000000
χ4822-2-2-2-22-12-22-11122-2-21-11−2i2i2i−2i1-1-1000000i3−i3−2i2i00i3−i3-1-111i−i−ii3−33−3000000003−3i−ii3−i30000000000
χ4922-2-2-2-22-12-22-111-2-2221-112i−2i−2i2i1-1-1000000−i3i3−2i2i00−i3i311-1-1−iii−i3−33−300000000−33i−ii3−i30000000000
χ5022-2-2-2-22-12-22-111-2-2221-112i−2i−2i2i1-1-1000000i3−i3−2i2i00i3−i311-1-1−iii−i−33−33000000003−3i−i−i3i30000000000
χ5122-2-2-2-22-12-22-111-2-2221-11−2i2i2i−2i1-1-1000000−i3i32i−2i00−i3i311-1-1i−i−ii−33−33000000003−3−iii3−i30000000000
χ5222-2-2-2-22-12-22-111-2-2221-11−2i2i2i−2i1-1-1000000i3−i32i−2i00i3−i311-1-1i−i−ii3−33−300000000−33−ii−i3i30000000000
χ5344444-4-44-4-4444400004-4-40000-4-4400000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-20000-222000022-20000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ5544444-4-4-2-4-44-2-2-20000-222000022-200000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ564444-44-444-4-44440000-4-440000-44-400000000000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-2-2-2000022-200002-22000000−2i32i300002i3−2i3000000000000000000000000000000000000
χ584444-44-4-24-4-4-2-2-2000022-200002-220000002i3−2i30000−2i32i3000000000000000000000000000000000000
χ594444-4-44-2-44-4-2-2-200002-2244-4-4-222000000000000000000-2-2220000000000000000000000000000
χ604444-4-44-2-44-4-2-2-200002-22-4-444-22200000000000000000022-2-20000000000000000000000000000
χ6144-4-4444-2-4-4-4-2220000-2-2-24i−4i4i−4i222000000000000000000−2i2i−2i2i0000000000000000000000000000
χ6244-4-4444-2-4-4-4-2220000-2-2-2−4i4i−4i4i2220000000000000000002i−2i2i−2i0000000000000000000000000000
χ6344-4-44-4-4-244-4-2220000-2220000-2-2200004-4-2-2000022000000000000000000000000000000000000
χ6444-4-44-4-4-244-4-2220000-2220000-2-220000-44220000-2-2000000000000000000000000000000000000
χ6544-4-4-44-4-2-444-222000022-20000-22-200000000004i−4i0000000000−2i−2i2i2i000000000000000000000000
χ6644-4-4-44-4-2-444-222000022-20000-22-20000000000−4i4i00000000002i2i−2i−2i000000000000000000000000
χ674-44i−4i0004000-44i−4i2-22i−2i000000000022−22−2i22i200000000002-22i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ684-44i−4i0004000-44i−4i2-22i−2i0000000000−22222i2−2i200000000002-22i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ694-44i−4i0004000-44i−4i-22−2i2i000000000022−22−2i22i20000000000-22−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ704-44i−4i0004000-44i−4i-22−2i2i0000000000−22222i2−2i20000000000-22−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ714-4−4i4i0004000-4−4i4i2-2−2i2i000000000022−222i2−2i200000000002-2−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ724-4−4i4i0004000-4−4i4i2-2−2i2i0000000000−2222−2i22i200000000002-2−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ734-4−4i4i0004000-4−4i4i-222i−2i000000000022−222i2−2i20000000000-222i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ744-4−4i4i0004000-4−4i4i-222i−2i0000000000−2222−2i22i20000000000-222i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ758-88i−8i000-40004−4i4i4-44i−4i000000000000000000000000-22−2i2i00000000000000000000000000000000
χ768-88i−8i000-40004−4i4i-44−4i4i0000000000000000000000002-22i−2i00000000000000000000000000000000
χ778-8−8i8i000-400044i−4i4-4−4i4i000000000000000000000000-222i−2i00000000000000000000000000000000
χ788-8−8i8i000-400044i−4i-444i−4i0000000000000000000000002-2−2i2i00000000000000000000000000000000

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