Finite Group Databasebeta

← Group #72228289

Character table — Group #72228289

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222666688888888888888881212181832323232323232323232323232323232364848484848484848144144144144144144144144
order12488224433661212121224242424242424248824336612121212242424242424242486612122424242424448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1
χ4111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111
χ52222222222-12-122-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-12-122-1-100000000
χ6222222222-12-12-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-12-1-12200000000
χ7222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-12-122-1-12222-1-1-1-12-1-1-1-1-1-1-1-100000000
χ8222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-12-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-100000000
χ9222-2-222222-12-122-1-1-2-2-2-21111-2-222-1-1-1-1-1-1-1-111111111-22-12-1-2-21100000000
χ10222-2-22222-12-12-1-1221111-2-2-2-2-2-222-1-1-1-1-1-1-1-111111111-2-12-1211-2-200000000
χ11222-2-22222-1-1-1-1-1-1-1-111111111-2-2222-12-122-1-1-2-2-2-21111-2-1-1-1-1111100000000
χ12222-2-22222-1-1-1-1-1-1-1-111111111-2-222-12-12-1-1221111-2-2-2-2-2-1-1-1-1111100000000
χ1322-200-2-2222222-2-2-2-200000000002-22222-2-2-2-2000000000-2-222000000000000
χ1422-200-2-2222-12-1-2-211000033−3−3002-2-1-1-1-1111133−3−333−3−30-212-1003−300000000
χ1522-200-2-2222-12-1-2-2110000−3−333002-2-1-1-1-11111−3−333−3−3330-212-100−3300000000
χ1622-200-2-222-12-1211-2-233−3−30000002-2-1-1-1-1111133−3−3−3−33301-2-123−30000000000
χ1722-200-2-222-12-1211-2-2−3−3330000002-2-1-1-1-11111−3−33333−3−301-2-12−330000000000
χ1822-200-2-222-1-1-1-1111133−3−333−3−3002-2-12-1211-2-2−3−3330000011-1-13−33−300000000
χ1922-200-2-222-1-1-1-1111133−3−3−3−333002-22-12-1-2-211000033−3−3011-1-13−3−3300000000
χ2022-200-2-222-1-1-1-11111−3−33333−3−3002-22-12-1-2-2110000−3−333011-1-1−333−300000000
χ2122-200-2-222-1-1-1-11111−3−333−3−333002-2-12-1211-2-233−3−30000011-1-1−33−3300000000
χ22333333-13-103030033000033333-1-1-10000000000000000-10-10-100-1-111-1-11-11-1
χ23333333-13-103030033000033333-1-1-10000000000000000-10-10-100-1-1-1-111-11-11
χ2433333-13-133030330033330000-13-1-10000000000000000-1-10-10-1-10011-1-1-11-11
χ2533333-13-133030330033330000-13-1-10000000000000000-1-10-10-1-100-1-1111-11-1
χ26333-3-33-13-1030300330000-3-3-3-3-31-1-1000000000000000010-10-100111-1-111-1-11
χ27333-3-33-13-1030300330000-3-3-3-3-31-1-1000000000000000010-10-10011-111-1-111-1
χ28333-3-3-13-1330303300-3-3-3-300001-3-1-100000000000000001-10-1011001-1-11-111-1
χ29333-3-3-13-1330303300-3-3-3-300001-3-1-100000000000000001-10-101100-111-11-1-11
χ30666666-26-20-30-300-3-30000-3-3-3-36-2-2-20000000000000000-20101001100000000
χ3166666-26-26-30-30-3-300-3-3-3-30000-26-2-20000000000000000-21010110000000000
χ32666-6-66-26-20-30-300-3-300003333-62-2-200000000000000002010100-1-100000000
χ33666-6-6-26-26-30-30-3-300333300002-6-2-2000000000000000021010-1-10000000000
χ3466-6002-6-266060-6-6000000000000-220000000000000000020-20000000000000
χ3566-6002-6-26-30-3033003333−33−33000000-2200000000000000000-1010−330000000000
χ3666-6002-6-26-30-303300−33−333333000000-2200000000000000000-10103−30000000000
χ3766-600-626-2060600-6-60000000000-2200000000000000000020-2000000000000
χ3866-600-626-20-30-3003300003333−33−3300-22000000000000000000-10100−3300000000
χ3966-600-626-20-30-300330000−33−33333300-22000000000000000000-101003−300000000
χ408-80−4i24i2000022-2-223−2323−232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ230000-121-23−300−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−i2i2−i2i200000000000000000
χ418-80−4i24i2000022-2-223−23−23232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ700002-1-21003−3i2−i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000
χ428-80−4i24i2000022-2-2−232323−232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ2300002-1-2100−33i2−i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000
χ438-80−4i24i2000022-2-2−2323−23232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ70000-121-2−3300−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−i2i2−i2i200000000000000000
χ448-80−4i24i200002-4-2423−23002ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ23−2i22i22i2−2i20000-1-111−33−33−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000
χ458-80−4i24i200002-4-24−2323002ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ7−2i22i22i2−2i20000-1-1113−33−3−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000
χ468-80−4i24i20000-424-20023−23−2i22i22i2−2i22ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ230000-1-111−333−3−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000
χ478-80−4i24i20000-424-200−2323−2i22i22i2−2i22ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ70000-1-1113−3−33−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000
χ488-80−4i24i20000-4-4440000−2i22i22i2−2i2−2i22i22i2−2i2000022-2-20000i2−i2−i2i2−i2i2−i2i200000000000000000
χ498-804i2−4i2000022-2-223−2323−23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ230000-121-23−300ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7i2−i2i2−i200000000000000000
χ508-804i2−4i2000022-2-223−23−2323−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ700002-1-21003−3−i2i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000
χ518-804i2−4i2000022-2-2−232323−23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ2300002-1-2100−33−i2i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000
χ528-804i2−4i2000022-2-2−2323−2323−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ70000-121-2−3300ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23i2−i2i2−i200000000000000000
χ538-804i2−4i200002-4-2423−2300−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232i2−2i2−2i22i20000-1-111−33−33ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000
χ548-804i2−4i200002-4-24−232300−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ72i2−2i2−2i22i20000-1-1113−33−3ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000
χ558-804i2−4i20000-424-20023−232i2−2i2−2i22i2−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ230000-1-111−333−3ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000
χ568-804i2−4i20000-424-200−23232i2−2i2−2i22i2−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ70000-1-1113−3−33ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000
χ578-804i2−4i20000-4-44400002i2−2i2−2i22i22i2−2i2−2i22i2000022-2-20000−i2i2i2−i2i2−i2i2−i200000000000000000
χ5899999-3-3-3-30000000000000000-3-31100000000000000001000000001111-1-1-1-1
χ5999999-3-3-3-30000000000000000-3-3110000000000000000100000000-1-1-1-11111
χ60999-9-9-3-3-3-3000000000000000033110000000000000000-1000000001-11-1-1-111
χ61999-9-9-3-3-3-3000000000000000033110000000000000000-100000000-11-1111-1-1
χ621818-180066-6-60000000000000000002-2000000000000000000000000000000000

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