Finite Group Databasebeta

← Group #13156038

Character table — Group #13156038

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order122233344666666666121212123336666666661212121212121212121212124412121212366612121212121222466668812121212121212121212121212122424242424242424242424242424242466666644881212121224242424412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200-200000022-2-2-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2002000000-2-22222-2-2-2-2222200000000000000000000000000000000000000
χ11222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ12222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-221111002222-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-200111100000000
χ13222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-122-2-1-1-1-100-2-2-2-21111111111000000000000000022-1-1-1-1-2-200111100000000
χ14222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2111100-2-2-2-211111111110000000000000000-2-211112200-1-1-1-100000000
χ15222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-222-1-1-1-1-1-1-1-111111100-2−i3−i3i3i30022-2-211-1-1-1-11111000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ16222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-222-1-1-1-1-1-1-1-111111100-2i3i3−i3−i30022-2-211-1-1-1-11111000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ17222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-2-21111-1-1-1-1111111002−i3−i3i3i300-2-222-1-11111-1-1-1-1000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ18222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-2-21111-1-1-1-1111111002i3i3−i3−i300-2-222-1-11111-1-1-1-1000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ1922222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1220222222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ2022222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-12202222-2-200000000000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ2122222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ2222222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-200000000000000-2-2-2-21111111111111111110000000000002-1-10
χ232222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1002000022-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ242222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-10020000-2-2-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ252222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-20000221111-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ262222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-20000-2-21111-2-2111111111111-2-2-2-21111111100000000220000-1-1-1-10000
χ272222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211222222-1-1-1-1-2-2111100-2000000-1-111-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000000033−3−30000
χ282222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211222222-1-1-1-1-2-2111100-2000000-1-111-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000000−3−3330000
χ292222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-2111100200000011-1-1221111-1-1-1-133−3−300003333−3−3−3−300000000000000−3−3330000
χ302222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-2111100200000011-1-1221111-1-1-1-1−3−3330000−3−3−3−333330000000000000033−3−30000
χ3122-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-20000000000002i−2i2i2i−2i−2i22-2-20000000000000−i2i22i−2i00002i2i−2i−2i0000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000002−200002−22−20000
χ3222-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-20000000000002i−2i2i2i−2i−2i22-2-20000000000000i2−i22i−2i00002i2i−2i−2i0000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−220000−22−220000
χ3322-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-2000000000000−2i2i−2i−2i2i2i22-2-20000000000000−i2i2−2i2i0000−2i−2i2i2i0000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−220000−22−220000
χ3422-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-2000000000000−2i2i−2i−2i2i2i22-2-20000000000000i2−i2−2i2i0000−2i−2i2i2i0000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000002−200002−22−20000
χ3522-2-2-122002-21-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−30000000−i2i2−ii−i3i300−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ3622-2-2-122002-21-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−30000000i2−i2−ii−i3i300−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ3722-2-2-122002-21-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−30000000−i2i2i−ii3−i300ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ3822-2-2-122002-21-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−30000000i2−i2i−ii3−i300ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ3922-2-2-122002-21-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−3330000000−i2i2−iii3−i300−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ4022-2-2-122002-21-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−3330000000i2−i2−iii3−i300−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ4122-2-2-122002-21-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−3330000000−i2i2i−i−i3i300ii−i−i−i3−i3i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ4222-2-2-122002-21-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−3330000000i2−i2i−i−i3i300ii−i−i−i3−i3i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ432-22-22222-2-2-222-2-2-22-222-2-2222-2-2-2-2222-2-22-22222-22-2-2-2-20000002-2-222-22-22-20000000000000000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ442-22-22222-2-2-222-2-2-22-222-2-2222-2-2-2-2222-2-22-22222-22-2-2-2-20000002-2-222-22-22-2000000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ452-22-2222-22-2-222-2-2-22-2-2-222222-2-2-2-2222-2-2-22-2-2-2-22-222220000002-2-22-22-22-222-202-22-2000000000000000000000000000000002-22-22-20000000000000000
χ462-22-2222-22-2-222-2-2-22-2-2-222222-2-2-2-2222-2-2-22-2-2-2-22-222220000002-2-22-22-22-22-220-22-2200000000000000000000000000000000-22-22-220000000000000000
χ472-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11222-11-11-2-2-2003−33−3-111-1-11-11-11000−i3i3i3−i30000003−33−33−33−33−3000000000000000000−i3i3i3−i32i−2i00−ii−ii00000000
χ482-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11222-11-11-2-2-2003−33−3-111-1-11-11-11000i3−i3−i3i30000003−33−33−33−33−3000000000000000000i3−i3−i3i3−2i2i00i−ii−i00000000
χ492-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11222-11-11-2-2-200−33−33-111-1-11-11-11000−i3i3i3−i3000000−33−33−33−33−33000000000000000000−i3i3i3−i3−2i2i00i−ii−i00000000
χ502-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11222-11-11-2-2-200−33−33-111-1-11-11-11000i3−i3−i3i3000000−33−33−33−33−33000000000000000000i3−i3−i3i32i−2i00−ii−ii00000000
χ512-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-1-2-2-21-11-1222003−33−3-111-11-11-11-12-20-11-11000000−333−33−3−33−3300000000000000002-2-11-1100003−3−3300000000
χ522-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-1-2-2-21-11-1222003−33−3-111-11-11-11-1-2201-11-1000000−333−33−3−33−330000000000000000-221-11-10000−333−300000000
χ532-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-1-2-2-21-11-122200−33−33-111-11-11-11-12-20-11-110000003−3−33−333−33−300000000000000002-2-11-110000−333−300000000
χ542-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-1-2-2-21-11-122200−33−33-111-11-11-11-1-2201-11-10000003−3−33−333−33−30000000000000000-221-11-100003−3−3300000000
χ552-22-22-12-221122-2-2-2-1-2-2-222-12-11111-12-1-2-2-22111-22-22-1-1-1000000-111-11-11-11-12-202-22-200000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-11-11-110000000000000−i3i30
χ562-22-22-12-221122-2-2-2-1-2-2-222-12-11111-12-1-2-2-22111-22-22-1-1-1000000-111-11-11-11-12-202-22-200000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-11-11-110000000000000i3−i30
χ572-22-22-12-221122-2-2-2-1-2-2-222-12-11111-12-1-2-2-22111-22-22-1-1-1000000-111-11-11-11-1-220-22-2200000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i31-11-11-10000000000000i3−i30
χ582-22-22-12-221122-2-2-2-1-2-2-222-12-11111-12-1-2-2-22111-22-22-1-1-1000000-111-11-11-11-1-220-22-2200000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i31-11-11-10000000000000−i3i30
χ5944444-24-4-4-2-244444-24-4-4-4-4-24-2-2-2-2-2-24-244-4-4222-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ6044444-2-244-2-24-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-20000001111111111440-2-2-2-200000000000000000000000000000000-2-211110000000000000000
χ6144444-2-244-2-24-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-20000001111111111-4-4022220000000000000000000000000000000022-1-1-1-10000000000000000
χ6244444-2-2-4-4-2-24-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-22222222222220000001111-1-1-1-1-1-1000−2i3−2i32i32i30000000000000000000000000000000000i3i3−i3−i30000000000000000
χ6344444-2-2-4-4-2-24-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-22222222222220000001111-1-1-1-1-1-10002i32i3−2i3−2i30000000000000000000000000000000000−i3−i3i3i30000000000000000
χ644444-24-24444-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2-21-211-2-24-2-211114-2-244-2-2-2-21111-2-21111004000000-2-2-2-2-2-21111111100000000000000000000000000000000000000
χ654444-24-24444-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2-21-211-2-24-2-211114-2-2-4-422221111-2-2111100-4000000222222-1-1-1-1-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.