Finite Group Databasebeta

← Group #10590340

Character table — Group #10590340

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12224444334444666666121212121212121236661212121212121212121212121212121212121212888888882424242424242424242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222-12222222-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ18222222222-12222222-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ19222222222-1-2-2-2-2222-1-1-122-1-122-1-1-1-1-1-1-2-211-2-211-1-1-1-111111111000022-2-200000000-1-1-1-1111100000000
χ20222222222-1-2-2-2-2222-1-1-122-1-122-1-1-1-1-1-1-2-211-2-211-1-1-1-1111111110000-2-222000000001111-1-1-1-100000000
χ2122222222-122222-1-1-1222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222-1-1-1222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ2322222222-12-2-2-2-2-1-1-1222-1-122-1-122-1-1-1-111-2-211-2-2-1-1-1-11111111122-2-20000-1-1-1-111110000000000000000
χ2422222222-12-2-2-2-2-1-1-1222-1-122-1-122-1-1-1-111-2-211-2-2-1-1-1-111111111-2-22200001111-1-1-1-10000000000000000
χ252222-2-2-2-22-122-2-2222-1-1-1-2-211-2-211-1-1-1-122-1-1-2-2111111-1-1-1-1111100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ262222-2-2-2-22-122-2-2222-1-1-1-2-211-2-211-1-1-1-122-1-1-2-2111111-1-1-1-111110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ272222-2-2-2-22-1-2-222222-1-1-1-2-211-2-211-1-1-1-1-2-21122-1-111111111-1-1-1-100002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ282222-2-2-2-22-1-2-222222-1-1-1-2-211-2-211-1-1-1-1-2-21122-1-111111111-1-1-1-10000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ292222-2-2-2-2-1222-2-2-1-1-122211-2-211-2-2-1-1-1-1-1-12211-2-21111-1-1-1-111112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ302222-2-2-2-2-1222-2-2-1-1-122211-2-211-2-2-1-1-1-1-1-12211-2-21111-1-1-1-11111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ312222-2-2-2-2-12-2-222-1-1-122211-2-211-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ322222-2-2-2-2-12-2-222-1-1-122211-2-211-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ3322-2-222-2-22200002-2-22-2-22222-2-2-2-222-2-20000000022-2-2000000000000000000000000000000002-22-20000
χ3422-2-222-2-22200002-2-22-2-22222-2-2-2-222-2-20000000022-2-200000000000000000000000000000000-22-220000
χ3522-2-2-2-2222200002-2-22-2-2-2-2-2-2222222-2-200000000-2-222000000000000000000000000000000002-2-220000
χ3622-2-2-2-2222200002-2-22-2-2-2-2-2-2222222-2-200000000-2-22200000000000000000000000000000000-222-20000
χ372-22-22i−2i2i−2i220000-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000000000000000000000000000002-22i−2i
χ382-22-22i−2i2i−2i220000-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i000000000000000000000000000000000000-22−2i2i
χ392-22-2−2i2i−2i2i220000-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000000000000000000000000000002-2−2i2i
χ402-22-2−2i2i−2i2i220000-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000000000000000000000000000000000-222i−2i
χ412-2-222i−2i−2i2i222i−2i2-2-2-22-2-222i−2i2i−2i−2i2i−2i2i2-2-222i−2i2i−2i2-22-22i−2i−2i2i2i2i−2i−2i22-2-200000000000000000000000000000000
χ422-2-222i−2i−2i2i22−2i2i-22-2-22-2-222i−2i2i−2i−2i2i−2i2i2-2-22−2i2i−2i2i-22-222i−2i−2i2i−2i−2i2i2i-2-22200000000000000000000000000000000
χ432-2-222i−2i−2i2i2-12i−2i2-2-2-2211-12i−2i−ii−2i2ii−i-111-12i−2i−ii2-2-11−iii−i−i−iii-1-1110000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ442-2-222i−2i−2i2i2-12i−2i2-2-2-2211-12i−2i−ii−2i2ii−i-111-12i−2i−ii2-2-11−iii−i−i−iii-1-1110000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ452-2-222i−2i−2i2i2-1−2i2i-22-2-2211-12i−2i−ii−2i2ii−i-111-1−2i2ii−i-221-1−iii−iii−i−i11-1-10000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ462-2-222i−2i−2i2i2-1−2i2i-22-2-2211-12i−2i−ii−2i2ii−i-111-1−2i2ii−i-221-1−iii−iii−i−i11-1-10000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ472-2-222i−2i−2i2i-122i−2i2-211-1-2-22−ii2i−2ii−i−2i2i-111-1−ii2i−2i-112-2−iii−i−i−iii-1-11100000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ482-2-222i−2i−2i2i-122i−2i2-211-1-2-22−ii2i−2ii−i−2i2i-111-1−ii2i−2i-112-2−iii−i−i−iii-1-11100000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ492-2-222i−2i−2i2i-12−2i2i-2211-1-2-22−ii2i−2ii−i−2i2i-111-1i−i−2i2i1-1-22−iii−iii−i−i11-1-100000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ502-2-222i−2i−2i2i-12−2i2i-2211-1-2-22−ii2i−2ii−i−2i2i-111-1i−i−2i2i1-1-22−iii−iii−i−i11-1-100000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ512-2-22−2i2i2i−2i222i−2i-22-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-2-222i−2i2i−2i-22-22−2i2i2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000
χ522-2-22−2i2i2i−2i22−2i2i2-2-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-2-22−2i2i−2i2i2-22-2−2i2i2i−2i−2i−2i2i2i22-2-200000000000000000000000000000000
χ532-2-22−2i2i2i−2i2-12i−2i-22-2-2211-1−2i2ii−i2i−2i−ii-111-12i−2i−ii-221-1i−i−ii−i−iii11-1-10000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ542-2-22−2i2i2i−2i2-12i−2i-22-2-2211-1−2i2ii−i2i−2i−ii-111-12i−2i−ii-221-1i−i−ii−i−iii11-1-10000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ552-2-22−2i2i2i−2i2-1−2i2i2-2-2-2211-1−2i2ii−i2i−2i−ii-111-1−2i2ii−i2-2-11i−i−iiii−i−i-1-1110000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ562-2-22−2i2i2i−2i2-1−2i2i2-2-2-2211-1−2i2ii−i2i−2i−ii-111-1−2i2ii−i2-2-11i−i−iiii−i−i-1-1110000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ572-2-22−2i2i2i−2i-122i−2i-2211-1-2-22i−i−2i2i−ii2i−2i-111-1−ii2i−2i1-1-22i−i−ii−i−iii11-1-100000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ582-2-22−2i2i2i−2i-122i−2i-2211-1-2-22i−i−2i2i−ii2i−2i-111-1−ii2i−2i1-1-22i−i−ii−i−iii11-1-100000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ592-2-22−2i2i2i−2i-12−2i2i2-211-1-2-22i−i−2i2i−ii2i−2i-111-1i−i−2i2i-112-2i−i−iiii−i−i-1-11100000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ602-2-22−2i2i2i−2i-12−2i2i2-211-1-2-22i−i−2i2i−ii2i−2i-111-1i−i−2i2i-112-2i−i−iiii−i−i-1-11100000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ6144444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-211111111111100000000000000000000000000000000
χ6244444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222221111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ634444-4-4-4-4-2-244-4-4-2-2-2-2-2-2222222221111-2-2-2-22222-1-1-1-11111-1-1-1-100000000000000000000000000000000
χ644444-4-4-4-4-2-2-4-444-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-1111100000000000000000000000000000000
χ6544-4-444-4-44-200004-4-4-22244-2-2-4-422-2-22200000000-2-2220000000000000000000000000000000000000000
χ6644-4-444-4-4-240000-2224-4-4-2-24422-4-4-2-22200000000-2-2220000000000000000000000000000000000000000
χ6744-4-444-4-4-2-20000-222-222-2-2-2-2222211-1-10000000011-1-13i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ6844-4-444-4-4-2-20000-222-222-2-2-2-2222211-1-10000000011-1-1−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ6944-4-4-4-4444-200004-4-4-222-4-42244-2-2-2-2220000000022-2-20000000000000000000000000000000000000000
χ7044-4-4-4-444-240000-2224-4-422-4-4-2-244-2-2220000000022-2-20000000000000000000000000000000000000000
χ7144-4-4-4-444-2-20000-222-2222222-2-2-2-211-1-100000000-1-1113i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
χ7244-4-4-4-444-2-20000-222-2222222-2-2-2-211-1-100000000-1-111−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000
χ734-44-44i−4i4i−4i4-20000-44-42-224i−4i−2i2i4i−4i−2i2i-22-2200000000−2i2i−2i2i0000000000000000000000000000000000000000
χ744-44-44i−4i4i−4i-2400002-22-44-4−2i2i4i−4i−2i2i4i−4i-22-2200000000−2i2i−2i2i0000000000000000000000000000000000000000
χ754-44-44i−4i4i−4i-2-200002-222-22−2i2i−2i2i−2i2i−2i2i1-11-100000000i−ii−i3-3-33−3i3i3i−3i00000000000000000000000000000000
χ764-44-44i−4i4i−4i-2-200002-222-22−2i2i−2i2i−2i2i−2i2i1-11-100000000i−ii−i-333-33i−3i−3i3i00000000000000000000000000000000
χ774-44-4−4i4i−4i4i4-20000-44-42-22−4i4i2i−2i−4i4i2i−2i-22-22000000002i−2i2i−2i0000000000000000000000000000000000000000
χ784-44-4−4i4i−4i4i-2400002-22-44-42i−2i−4i4i2i−2i−4i4i-22-22000000002i−2i2i−2i0000000000000000000000000000000000000000
χ794-44-4−4i4i−4i4i-2-200002-222-222i−2i2i−2i2i−2i2i−2i1-11-100000000−ii−ii3-3-333i−3i−3i3i00000000000000000000000000000000
χ804-44-4−4i4i−4i4i-2-200002-222-222i−2i2i−2i2i−2i2i−2i1-11-100000000−ii−ii-333-3−3i3i3i−3i00000000000000000000000000000000
χ814-4-444i−4i−4i4i-2-24i−4i4-422-222-2−2i2i−2i2i2i−2i2i−2i1-1-11−2i2i−2i2i-22-22i−i−iiii−i−i11-1-100000000000000000000000000000000
χ824-4-444i−4i−4i4i-2-2−4i4i-4422-222-2−2i2i−2i2i2i−2i2i−2i1-1-112i−2i2i−2i2-22-2i−i−ii−i−iii-1-11100000000000000000000000000000000
χ834-4-44−4i4i4i−4i-2-24i−4i-4422-222-22i−2i2i−2i−2i2i−2i2i1-1-11−2i2i−2i2i2-22-2−iii−iii−i−i-1-11100000000000000000000000000000000
χ844-4-44−4i4i4i−4i-2-2−4i4i4-422-222-22i−2i2i−2i−2i2i−2i2i1-1-112i−2i2i−2i-22-22−iii−i−i−iii11-1-100000000000000000000000000000000

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