Finite Group Databasebeta

← Group #10826080

Character table — Group #10826080

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order124422234446888888881212242424246661212122424242424244444448888881212121212121212121212122424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ511111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ9111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ10111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ11111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-111-1-1-1-1
χ12111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1-111-1-11111
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1111111
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-111
χ172222222-1222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ192222222-1222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-21111-1-1-1-111111111-1-1-1-111110000000000000000
χ202222222-1222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22211111111-1-1-1-111111111-1-1-1-10000000000000000
χ212222222-1222-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-11111112222-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-10000000000000000
χ222222222-1222-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-111111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ232222222-1222-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ242222222-1222-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2-2-2-2-2222222111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2522222-2-222-2-222222-2-2-2-22222222-2-22-2-222-2-2-2-2002i−2i00002i−2i0000002i2i−2i−2i000000002i2i−2i−2i00000000000000000000
χ2622222-2-222-2-222222-2-2-2-22222222-2-22-2-222-2-2-2-200−2i2i0000−2i2i000000−2i−2i2i2i00000000−2i−2i2i2i00000000000000000000
χ2722222-2-222-2-22-2-2-2-2222222-2-2-2-22-2-22-2-2-2-22222002i−2i0000−2i2i0000002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ2822222-2-222-2-22-2-2-2-2222222-2-2-2-22-2-22-2-2-2-2222200−2i2i00002i−2i000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ2922222-2-2-12-2-2-12222-2-2-2-2-1-1-1-1-1-1-111-111-1-11111002i−2i00002i−2i00−i3−i3i3i3−i−iii33−3−3−i3−i3i3i3−i−iii33−3−30000000000000000
χ3022222-2-2-12-2-2-12222-2-2-2-2-1-1-1-1-1-1-111-111-1-11111002i−2i00002i−2i00i3i3−i3−i3−i−iii−3−333i3i3−i3−i3−i−iii−3−3330000000000000000
χ3122222-2-2-12-2-2-12222-2-2-2-2-1-1-1-1-1-1-111-111-1-1111100−2i2i0000−2i2i00−i3−i3i3i3ii−i−i−3−333−i3−i3i3i3ii−i−i−3−3330000000000000000
χ3222222-2-2-12-2-2-12222-2-2-2-2-1-1-1-1-1-1-111-111-1-1111100−2i2i0000−2i2i00i3i3−i3−i3ii−i−i33−3−3i3i3−i3−i3ii−i−i33−3−30000000000000000
χ3322222-2-2-12-2-2-1-2-2-2-22222-1-11111-111-11111-1-1-1-1002i−2i0000−2i2i00−i3−i3i3i3−i−iii−3−333i3i3−i3−i3ii−i−i33−3−30000000000000000
χ3422222-2-2-12-2-2-1-2-2-2-22222-1-11111-111-11111-1-1-1-1002i−2i0000−2i2i00i3i3−i3−i3−i−iii33−3−3−i3−i3i3i3ii−i−i−3−3330000000000000000
χ3522222-2-2-12-2-2-1-2-2-2-22222-1-11111-111-11111-1-1-1-100−2i2i00002i−2i00−i3−i3i3i3ii−i−i33−3−3i3i3−i3−i3−i−iii−3−3330000000000000000
χ3622222-2-2-12-2-2-1-2-2-2-22222-1-11111-111-11111-1-1-1-100−2i2i00002i−2i00i3i3−i3−i3ii−i−i−3−333−i3−i3i3i3−i−iii33−3−30000000000000000
χ372222-22-22-22-2222-2-222-2-2222222-22-2-22-2-2-222-2-22i−2i00002i−2i00002i−2i2i−2i000000002i−2i2i−2i000000000000000000000000
χ382222-22-22-22-2222-2-222-2-2222222-22-2-22-2-2-222-2-2−2i2i0000−2i2i0000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000000000
χ392222-22-22-22-22-2-222-2-22222-2-2-2-2-22-2-22-222-2-2222i−2i0000−2i2i00002i−2i2i−2i00000000−2i2i−2i2i000000000000000000000000
χ402222-22-22-22-22-2-222-2-22222-2-2-2-2-22-2-22-222-2-222−2i2i00002i−2i0000−2i2i−2i2i000000002i−2i2i−2i000000000000000000000000
χ412222-22-2-1-22-2-122-2-222-2-2-1-1-1-1-1-11-111-1111-1-1112i−2i00002i−2i0000−ii−ii−i3i3−i3i33−33−3−ii−ii−i3i3−i3i33−33−30000000000000000
χ422222-22-2-1-22-2-122-2-222-2-2-1-1-1-1-1-11-111-1111-1-1112i−2i00002i−2i0000−ii−iii3−i3i3−i3−33−33−ii−iii3−i3i3−i3−33−330000000000000000
χ432222-22-2-1-22-2-122-2-222-2-2-1-1-1-1-1-11-111-1111-1-111−2i2i0000−2i2i0000i−ii−i−i3i3−i3i3−33−33i−ii−i−i3i3−i3i3−33−330000000000000000
χ442222-22-2-1-22-2-122-2-222-2-2-1-1-1-1-1-11-111-1111-1-111−2i2i0000−2i2i0000i−ii−ii3−i3i3−i33−33−3i−ii−ii3−i3i3−i33−33−30000000000000000
χ452222-22-2-1-22-2-1-2-222-2-222-1-111111-111-11-1-111-1-12i−2i0000−2i2i0000−ii−ii−i3i3−i3i3−33−33i−ii−ii3−i3i3−i33−33−30000000000000000
χ462222-22-2-1-22-2-1-2-222-2-222-1-111111-111-11-1-111-1-12i−2i0000−2i2i0000−ii−iii3−i3i3−i33−33−3i−ii−i−i3i3−i3i3−33−330000000000000000
χ472222-22-2-1-22-2-1-2-222-2-222-1-111111-111-11-1-111-1-1−2i2i00002i−2i0000i−ii−i−i3i3−i3i33−33−3−ii−iii3−i3i3−i3−33−330000000000000000
χ482222-22-2-1-22-2-1-2-222-2-222-1-111111-111-11-1-111-1-1−2i2i00002i−2i0000i−ii−ii3−i3i3−i3−33−33−ii−ii−i3i3−i3i33−33−30000000000000000
χ492222-2-222-2-22222-2-2-2-222222222-2-22-2-22-2-2-2-22200002-200002-2000000002-2-22000000002-2-220000000000000000
χ502222-2-222-2-22222-2-2-2-222222222-2-22-2-22-2-2-2-2220000-220000-2200000000-222-200000000-222-20000000000000000
χ512222-2-222-2-222-2-22222-2-222-2-2-2-2-2-22-2-222222-2-200002-20000-22000000002-2-2200000000-222-20000000000000000
χ522222-2-222-2-222-2-22222-2-222-2-2-2-2-2-22-2-222222-2-20000-2200002-200000000-222-2000000002-2-220000000000000000
χ532222-2-22-1-2-22-122-2-2-2-222-1-1-1-1-1-111-111-11111-1-100002-200002-23−3−33−333−3-111-13−3−33−333−3-111-10000000000000000
χ542222-2-22-1-2-22-122-2-2-2-222-1-1-1-1-1-111-111-11111-1-100002-200002-2−333−33−3−33-111-1−333−33−3−33-111-10000000000000000
χ552222-2-22-1-2-22-122-2-2-2-222-1-1-1-1-1-111-111-11111-1-10000-220000-223−3−333−3−331-1-113−3−333−3−331-1-110000000000000000
χ562222-2-22-1-2-22-122-2-2-2-222-1-1-1-1-1-111-111-11111-1-10000-220000-22−333−3−333−31-1-11−333−3−333−31-1-110000000000000000
χ572222-2-22-1-2-22-1-2-22222-2-2-1-1111111-111-1-1-1-1-11100002-20000-223−3−333−3−33-111-1−333−3−333−31-1-110000000000000000
χ582222-2-22-1-2-22-1-2-22222-2-2-1-1111111-111-1-1-1-1-11100002-20000-22−333−3−333−3-111-13−3−333−3−331-1-110000000000000000
χ592222-2-22-1-2-22-1-2-22222-2-2-1-1111111-111-1-1-1-1-1110000-2200002-23−3−33−333−31-1-11−333−33−3−33-111-10000000000000000
χ602222-2-22-1-2-22-1-2-22222-2-2-1-1111111-111-1-1-1-1-1110000-2200002-2−333−33−3−331-1-113−3−33−333−3-111-10000000000000000
χ6122-2-22222-2-2-222i−2i2i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i00000000000000000000000000000000000000002-20000002i−2i00
χ6222-2-22222-2-2-222i−2i2i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000-22000000−2i2i00
χ6322-2-22222-2-2-22−2i2i−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000002-2000000−2i2i00
χ6422-2-22222-2-2-22−2i2i−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000-220000002i−2i00
χ6522-2-22-2-22-22222i−2i2i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i000000000000000000000000000000000000020-20000002i−2i0000
χ6622-2-22-2-22-22222i−2i2i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i0000000000000000000000000000000000000-202000000−2i2i0000
χ6722-2-22-2-22-2222−2i2i−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i000000000000000000000000000000000000020-2000000−2i2i0000
χ6822-2-22-2-22-2222−2i2i−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i0000000000000000000000000000000000000-2020000002i−2i0000
χ6922-2-2-22-222-2222i−2i−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i00000000000000000000000000000000000020-2000002i−2i000000
χ7022-2-2-22-222-2222i−2i−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i000000000000000000000000000000000000-20200000−2i2i000000
χ7122-2-2-22-222-222−2i2i2i−2i−2i2i2i−2i-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i00000000000000000000000000000000000020-200000−2i2i000000
χ7222-2-2-22-222-222−2i2i2i−2i−2i2i2i−2i-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i000000000000000000000000000000000000-202000002i−2i000000
χ7322-2-2-2-22222-222i−2i−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i0000000000000000000000000000000000000000002-20000002i−2i
χ7422-2-2-2-22222-222i−2i−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i000000000000000000000000000000000000000000-22000000−2i2i
χ7522-2-2-2-22222-22−2i2i2i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i0000000000000000000000000000000000000000002-2000000−2i2i
χ7622-2-2-2-22222-22−2i2i2i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i000000000000000000000000000000000000000000-220000002i−2i
χ7744-4-4444-2-4-4-4-24i−4i4i−4i4i−4i4i−4i22−2i−2i2i2i-2-2-2222−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ7844-4-4444-2-4-4-4-2−4i4i−4i4i−4i4i−4i4i222i2i−2i−2i-2-2-22222i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ7944-4-44-4-4-2-444-24i−4i4i−4i−4i4i−4i4i22−2i−2i2i2i-2222-2-2−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8044-4-44-4-4-2-444-2−4i4i−4i4i4i−4i4i−4i222i2i−2i−2i-2222-2-22i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8144-4-4-44-4-24-44-24i−4i−4i4i4i−4i−4i4i22−2i−2i2i2i2-22-22-22i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8244-4-4-44-4-24-44-2−4i4i4i−4i−4i4i4i−4i222i2i−2i−2i2-22-22-2−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-244-4-24i−4i−4i4i−4i4i4i−4i22−2i−2i2i2i22-2-2-222i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8444-4-4-4-44-244-4-2−4i4i4i−4i4i−4i−4i4i222i2i−2i−2i22-2-2-22−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ858-88i−8i0008000-8000000008i−8i00000000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i000-4000400000000−4i4i−4ζ7+4ζ234ζ7−4ζ234ζ5−4ζ13−4ζ5+4ζ130000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i000-4000400000000−4i4i4ζ7−4ζ23−4ζ7+4ζ23−4ζ5+4ζ134ζ5−4ζ130000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i0008000-800000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-40004000000004i−4i4ζ5−4ζ13−4ζ5+4ζ13−4ζ7+4ζ234ζ7−4ζ230000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-40004000000004i−4i−4ζ5+4ζ134ζ5−4ζ134ζ7−4ζ23−4ζ7+4ζ230000000000000000000000000000000000000000000000000000000000000000

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