Finite Group Databasebeta

← Group #10699227

Character table — Group #10699227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222344446664444661212121212121212888812122424242424242424246688121224242424444488882488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ9222222222-2-22222-2-2-222-2-2-222-2-2-20000-220000000000002i−2i002i2i−2i−2i000000000000
χ10222222222-2-22222-2-2-222-2-2-222-2-2-20000-22000000000000−2i2i00−2i−2i2i2i000000000000
χ112222222-2-222222-22-2-222222-2-2-2-220000-2-200000000000000000000000000002-200
χ122222222-2-222222-22-2-222222-2-2-2-220000-2-20000000000000000000000000000-2200
χ132222222-2-2-2-2222-2-22222-2-2-2-2-222-200002-200000000000000000000000022-2-20000
χ142222222-2-2-2-2222-2-22222-2-2-2-2-222-200002-2000000000000000000000000-2-2220000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-1000000000000
χ19222222-122-2-2-1-1-12-2-2-2-1-1111-1-111100001-13333−3−3−3−300−i3i32i−2i−i3i3−i−iii000000000000
χ20222222-122-2-2-1-1-12-2-2-2-1-1111-1-111100001-13333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i000000000000
χ21222222-122-2-2-1-1-12-2-2-2-1-1111-1-111100001-1−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i000000000000
χ22222222-122-2-2-1-1-12-2-2-2-1-1111-1-111100001-1−3−3−3−3333300i3−i32i−2ii3−i3−i−iii000000000000
χ232222-2-222222222-2-2-22-2-22-2-222-2-2200002-20000000000000000000000000000002-2
χ242222-2-222222222-2-2-22-2-22-2-222-2-2200002-2000000000000000000000000000000-22
χ252222-2-2222-2-2222-222-2-2-2-2222222-20000-2-2000000000000000000002i2i−2i−2i00000000
χ262222-2-2222-2-2222-222-2-2-2-2222222-20000-2-200000000000000000000−2i−2i2i2i00000000
χ272222-2-22-2-2222222-22-2-2-22-2-2-2-22220000-22000000002-22200-2-20000000000000000
χ282222-2-22-2-2222222-22-2-2-22-2-2-2-22220000-2200000000-22-2-200220000000000000000
χ292222-2-22-2-2-2-222222-22-2-2-222-2-2-2-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-22-2-2-2-222222-22-2-2-222-2-2-2-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-2-1-2-222-1-1-12-22-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i32-2-1-10011−i3i3−i3i3000000000000
χ322222-2-2-1-2-222-1-1-12-22-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i3-221100-1-1i3−i3i3−i3000000000000
χ332222-2-2-1-2-222-1-1-12-22-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i32-2-1-10011i3−i3i3−i3000000000000
χ342222-2-2-1-2-222-1-1-12-22-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i3-221100-1-1−i3i3−i3i3000000000000
χ352222-2-2-1-2-2-2-2-1-1-122-22111-1-1111112i2i−2i−2i-1-1−i−iii−i−iii00−i3i300i3−i33−3−33000000000000
χ362222-2-2-1-2-2-2-2-1-1-122-22111-1-1111112i2i−2i−2i-1-1−i−iii−i−iii00i3−i300−i3i3−333−3000000000000
χ372222-2-2-1-2-2-2-2-1-1-122-22111-1-111111−2i−2i2i2i-1-1ii−i−iii−i−i00−i3i300i3−i3−333−3000000000000
χ382222-2-2-1-2-2-2-2-1-1-122-22111-1-111111−2i−2i2i2i-1-1ii−i−iii−i−i00i3−i300−i3i33−3−33000000000000
χ39444444-2-4-444-2-2-2-44-4-4-2-2-2-2-22222-200002200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-222222-2-220000-2200000000000000000000000000000000
χ414444-4-4-24444-2-2-2-4-4-4422-222-2-222-20000-2200000000000000000000000000000000
χ424444-4-4-244-4-4-2-2-2-444-4222-2-2-2-2-2-2200002200000000000000000000000000000000
χ4344-4-40044i−4i004-4-40000000004i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ4444-4-40044i−4i004-4-40000000004i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ4544-4-4004−4i4i004-4-4000000000−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ4644-4-4004−4i4i004-4-4000000000−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ4744-4-400-24i−4i00-222000000023−23−2i2i−2i32i302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23000000000000000000000000
χ4844-4-400-24i−4i00-222000000023−23−2i2i−2i32i30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23000000000000000000000000
χ4944-4-400-24i−4i00-2220000000−2323−2i2i2i3−2i302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23000000000000000000000000
χ5044-4-400-24i−4i00-2220000000−2323−2i2i2i3−2i30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23000000000000000000000000
χ5144-4-400-2−4i4i00-222000000023−232i−2i2i3−2i30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23000000000000000000000000
χ5244-4-400-2−4i4i00-222000000023−232i−2i2i3−2i302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23000000000000000000000000
χ5344-4-400-2−4i4i00-2220000000−23232i−2i−2i32i30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23000000000000000000000000
χ5444-4-400-2−4i4i00-2220000000−23232i−2i−2i32i302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23000000000000000000000000
χ554-44-44-440000-4-4400004-40000000000000000000000000000000000000000−2i22i20000
χ564-44-44-440000-4-4400004-400000000000000000000000000000000000000002i2−2i20000
χ574-44-4-4440000-4-440000-440000000000000000000000000000000000000022−22000000
χ584-44-4-4440000-4-440000-4400000000000000000000000000000000000000−2222000000
χ594-4-44004004-4-44-40000004000000-4000000000000000000000000002i−2i2i−2i00000000
χ604-4-44004004-4-44-40000004000000-400000000000000000000000000−2i2i−2i2i00000000
χ614-4-4400400-44-44-4000000-40000004000000000000000000000000002-2-2200000000
χ624-4-4400400-44-44-4000000-4000000400000000000000000000000000-222-200000000
χ638-88-88-8-4000044-40000-440000000000000000000000000000000000000000000000
χ648-88-8-88-4000044-400004-40000000000000000000000000000000000000000000000
χ658-8-8800-4008-84-44000000-4000000400000000000000000000000000000000000000
χ668-8-8800-400-884-440000004000000-400000000000000000000000000000000000000

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