Finite Group Databasebeta

← Group #13146889

Character table — Group #13146889

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1122233333333334444666666666661212121212121212121212121212242424242424363636363636363636363636484848484848484848727272727272
order12346223366666626612466666612121212266666666661212123336668888242424242424242466666612121224661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ3111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1
χ4111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ51111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ61111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i32
χ71111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-11111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321−i321+i321−i32
χ81111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-11111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ91111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ101111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i32
χ111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-11111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321+i321−i321+i32
χ121111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-11111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ1322222222222222222222222222222222222222222222-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1000000
χ14222222222222222-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2222-1-1-1-1-1-1000000000000111111-1-1-1000000
χ152222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32222222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3222−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i32−1−i3−1+i3-11+i321−i32-11+i321−i32000000000000-1-11+i321+i321−i321−i32-11+i321−i32000000
χ162222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-2-22222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-21+i31+i31+i31+i31−i31−i31−i31−i32−1−i3−1+i3-11+i321−i32-11+i321−i3200000000000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000
χ172222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32222222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3222−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i32−1+i3−1−i3-11−i321+i32-11−i321+i32000000000000-1-11−i321−i321+i321+i32-11−i321+i32000000
χ182222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-2-22222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-2-21−i31−i31−i31−i31+i31+i31+i31+i32−1+i3−1−i3-11−i321+i32-11−i321+i3200000000000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000
χ19222-222222222222000-2-2222222-2-2-2-200000000000-2-2-2222222000000000000000000-2-2-2000000
χ20222-222222222222000-2-2222222-2-2-2-200000000000-2-2-2-1-1-1-1-1-1000000000000−i3i3−i3i3−i3i3111000000
χ21222-222222222222000-2-2222222-2-2-2-200000000000-2-2-2-1-1-1-1-1-1000000000000i3−i3i3−i3i3−i3111000000
χ22222-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000-2-222−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i300000000000-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000-21+i31−i3000000
χ23222-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000-2-222−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i300000000000-21+i31−i3-11+i321−i32-11+i321−i32000000000000−i3i3−3+i323−i323+i32−3−i321−1−i32−1+i32000000
χ24222-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000-2-222−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i300000000000-21+i31−i3-11+i321−i32-11+i321−i32000000000000i3−i33−i32−3+i32−3−i323+i321−1−i32−1+i32000000
χ25222-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000-2-222−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i300000000000-21−i31+i32−1+i3−1−i32−1+i3−1−i3000000000000000000-21−i31+i3000000
χ26222-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000-2-222−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i300000000000-21−i31+i3-11−i321+i32-11−i321+i32000000000000−i3i33+i32−3−i32−3+i323−i321−1+i32−1−i32000000
χ27222-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000-2-222−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i300000000000-21−i31+i3-11−i321+i32-11−i321+i32000000000000i3−i3−3−i323+i323−i32−3+i321−1+i32−1−i32000000
χ282-220-2-2222-2-2-2-222000002-22-22-2000000000000000000222-2-2-22−22−222−2−222−2−2000000000000000
χ292-220-2-2222-2-2-2-222000002-22-22-2000000000000000000222-2-2-2−22−22−2−222−2−222000000000000000
χ302-220-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000002-2−1−i31+i3−1+i31−i30000000000000000002−1−i3−1+i3-21+i31−i32−22−2−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23000000000000000
χ312-220-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000002-2−1−i31+i3−1+i31−i30000000000000000002−1−i3−1+i3-21+i31−i3−22−22ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23000000000000000
χ322-220-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000002-2−1+i31−i3−1−i31+i30000000000000000002−1+i3−1−i3-21−i31+i32−22−2ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13000000000000000
χ332-220-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000002-2−1+i31−i3−1−i31+i30000000000000000002−1+i3−1−i3-21−i31+i3−22−22−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13000000000000000
χ3433333-1-133-1-133-1-13333-1-1-1-1-1-1-13-13-1-1-1-13-1-1-13-1-1-1-1-1-100000011-1-11-11-11-11-10000000001-111-1-1
χ3533333-1-133-1-133-1-13333-1-1-1-1-1-1-13-13-1-1-1-13-1-1-13-1-1-1-1-1-1000000-1-111-11-11-11-11000000000-11-1-111
χ3633333-1-133-1-133-1-1-3-3-33-1-1-1-1-1-1-13-13-1111-3111-3111-1-1-100000011-1-11-11-11-11-1000000000-11-1-111
χ3733333-1-133-1-133-1-1-3-3-33-1-1-1-1-1-1-13-13-1111-3111-3111-1-1-1000000-1-111-11-11-11-110000000001-111-1-1
χ3833333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i323333-1-1-11+i321+i321−i321−i32−3−3i321+i32−3+3i321−i32-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-11+i321−i3200000011-1-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i320000000001-1−1−i32−1+i321+i321−i32
χ3933333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i323333-1-1-11+i321+i321−i321−i32−3−3i321+i32−3+3i321−i32-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32-11+i321−i32000000-1-1111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32000000000-111+i321−i32−1−i32−1+i32
χ4033333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-3-3-33-1-1-11+i321+i321−i321−i32−3−3i321+i32−3+3i321−i321113+3i32−1−i32−1−i32−1−i323−3i32−1+i32−1+i32−1+i32-11+i321−i3200000011-1-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32000000000-111+i321−i32−1−i32−1+i32
χ4133333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-3-3-33-1-1-11+i321+i321−i321−i32−3−3i321+i32−3+3i321−i321113+3i32−1−i32−1−i32−1−i323−3i32−1+i32−1+i32−1+i32-11+i321−i32000000-1-1111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i320000000001-1−1−i32−1+i321+i321−i32
χ4233333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i323333-1-1-11−i321−i321+i321+i32−3+3i321−i32−3−3i321+i32-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-11−i321+i3200000011-1-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i320000000001-1−1+i32−1−i321−i321+i32
χ4333333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i323333-1-1-11−i321−i321+i321+i32−3+3i321−i32−3−3i321+i32-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32-11−i321+i32000000-1-1111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32000000000-111−i321+i32−1+i32−1−i32
χ4433333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-3-3-33-1-1-11−i321−i321+i321+i32−3+3i321−i32−3−3i321+i321113−3i32−1+i32−1+i32−1+i323+3i32−1−i32−1−i32−1−i32-11−i321+i3200000011-1-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32000000000-111−i321+i32−1+i32−1−i32
χ4533333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-3-3-33-1-1-11−i321−i321+i321+i32−3+3i321−i32−3−3i321+i321113−3i32−1+i32−1+i32−1+i323+3i32−1−i32−1−i32−1−i32-11−i321+i32000000-1-1111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i320000000001-1−1+i32−1−i321−i321+i32
χ464-440-4-4444-4-4-4-444000004-44-44-4000000000000000000-2-2-2222000000000000000000000000000
χ474-440-4-44−2−2i3−2+2i32+2i32−2i32+2i32−2i3−2−2i3−2+2i3000004-4−2−2i32+2i3−2+2i32−2i3000000000000000000-21+i31−i32−1−i3−1+i3000000000000000000000000000
χ484-440-4-44−2+2i3−2−2i32−2i32+2i32−2i32+2i3−2+2i3−2−2i3000004-4−2+2i32−2i3−2−2i32+2i3000000000000000000-21−i31+i32−1+i3−1−i3000000000000000000000000000
χ49666-66-2-266-2-266-2-2000-62-2-2-2-2-2-2-62-6200000000000222000000000000000000000000000000000
χ50666-66-2-2−3−3i3−3+3i31+i31−i3−3−3i3−3+3i31+i31−i3000-62-2-21+i31+i31−i31−i33+3i3−1−i33−3i3−1+i3000000000002−1−i3−1+i3000000000000000000000000000000000
χ51666-66-2-2−3+3i3−3−3i31−i31+i3−3+3i3−3−3i31−i31+i3000-62-2-21−i31−i31+i31+i33−3i3−1+i33+3i3−1−i3000000000002−1+i3−1−i3000000000000000000000000000000000
χ5266-36-366000000006-3-3-36-3-3000000006-3-300000000-300000000000000000000000000000000000
χ5366-36-36600000000-633-36-3-300000000-63300000000-300000000000000000000000000000000000
χ5466-36-3-2-2004400446-3-3-3-211-2-2-2-20404-21104-2-204-2-21-2-2000000000000000000000000000000000
χ5566-36-3-2-200440044-633-3-211-2-2-2-204042-1-10-4220-4221-2-2000000000000000000000000000000000
χ5666-36-3-2-200−2−2i3−2+2i300−2−2i3−2+2i36-3-3-3-2111+i31+i31−i31−i30−2−2i30−2+2i3-2110−2−2i31+i31+i30−2+2i31−i31−i311+i31−i3000000000000000000000000000000000
χ5766-36-3-2-200−2−2i3−2+2i300−2−2i3−2+2i3-633-3-2111+i31+i31−i31−i30−2−2i30−2+2i32-1-102+2i3−1−i3−1−i302−2i3−1+i3−1+i311+i31−i3000000000000000000000000000000000
χ5866-36-3-2-200−2+2i3−2−2i300−2+2i3−2−2i36-3-3-3-2111−i31−i31+i31+i30−2+2i30−2−2i3-2110−2+2i31−i31−i30−2−2i31+i31+i311−i31+i3000000000000000000000000000000000
χ5966-36-3-2-200−2+2i3−2−2i300−2+2i3−2−2i3-633-3-2111−i31−i31+i31+i30−2+2i30−2−2i32-1-102−2i3−1+i3−1+i302+2i3−1−i3−1−i311−i31+i3000000000000000000000000000000000
χ6066-3-6-366000000000−3i33i33-6-3-3000000000−3i33i300000000300000000000000000000000000000000000
χ6166-3-6-3660000000003i3−3i33-6-3-30000000003i3−3i300000000300000000000000000000000000000000000
χ6266-3-6-3-2-2004400440−3i33i33211-2-2-2-20-40-40i3−i300−2i32i300−2i32i3-122000000000000000000000000000000000
χ6366-3-6-3-2-20044004403i3−3i33211-2-2-2-20-40-40−i3i3002i3−2i3002i3−2i3-122000000000000000000000000000000000
χ6466-3-6-3-2-200−2−2i3−2+2i300−2−2i3−2+2i30−3i33i332111+i31+i31−i31−i302+2i302−2i30i3−i300−3+i33−i3003+i3−3−i3-1−1−i3−1+i3000000000000000000000000000000000
χ6566-3-6-3-2-200−2−2i3−2+2i300−2−2i3−2+2i303i3−3i332111+i31+i31−i31−i302+2i302−2i30−i3i3003−i3−3+i300−3−i33+i3-1−1−i3−1+i3000000000000000000000000000000000
χ6666-3-6-3-2-200−2+2i3−2−2i300−2+2i3−2−2i30−3i33i332111−i31−i31+i31+i302−2i302+2i30i3−i3003+i3−3−i300−3+i33−i3-1−1+i3−1−i3000000000000000000000000000000000
χ6766-3-6-3-2-200−2+2i3−2−2i300−2+2i3−2−2i303i3−3i332111−i31−i31+i31+i302−2i302+2i30−i3i300−3−i33+i3003−i3−3+i3-1−1+i3−1−i3000000000000000000000000000000000
χ686-660-62-26622-6-6-2-200000-22-22-220000000000000000000000002−2−222−2−222−2−22000000000000000
χ696-660-62-26622-6-6-2-200000-22-22-22000000000000000000000000−222−2−222−2−222−2000000000000000
χ706-660-62-2−3−3i3−3+3i3−1−i3−1+i33+3i33−3i31+i31−i300000-221+i3−1−i31−i3−1+i30000000000000000000000002−2−22−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000000000000
χ716-660-62-2−3−3i3−3+3i3−1−i3−1+i33+3i33−3i31+i31−i300000-221+i3−1−i31−i3−1+i3000000000000000000000000−222−2ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000000000000
χ726-660-62-2−3+3i3−3−3i3−1+i3−1−i33−3i33+3i31−i31+i300000-221−i3−1+i31+i3−1−i30000000000000000000000002−2−22ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000000000000
χ736-660-62-2−3+3i3−3−3i3−1+i3−1−i33−3i33+3i31−i31+i300000-221−i3−1+i31+i3−1−i3000000000000000000000000−222−2−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000000000000
χ7412-12-6064-400-8-80088000002-2-44-44000000000000000000000000000000000000000000000000000
χ7512-12-6064-4004+4i34−4i300−4−4i3−4+4i3000002-22+2i3−2−2i32−2i3−2+2i3000000000000000000000000000000000000000000000000000
χ7612-12-6064-4004−4i34+4i300−4+4i3−4−4i3000002-22−2i3−2+2i32+2i3−2−2i3000000000000000000000000000000000000000000000000000
χ7712-12-606-12120000000000000-660000000000000000000000000000000000000000000000000000000

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