Finite Group Databasebeta

← Group #13088732

Character table — Group #13088732

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222224444444558888888888888888810101010101010151515151818202020202030303030303030303030303030306060606072729090
order123346612123561012121222151515152030303030606060606060606046666121244442266121212444444121212121212121212121212101022
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ51111111111111111-1-111111111111111111-1-1-1-1-1-1-1ii−i−i11-1-1-1-1-1i−iii−i−iiiii−i−i−i−iii−i−i11-1-1
χ61111111111111111-1-111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1i−i−i−iiiiiii−i−i−i−i−i−iii-1-111
χ71111111111111111-1-111111111111111111-1-1-1-1-1-1-1−i−iii11-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−iii11-1-1
χ81111111111111111-1-111111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1−iiii−i−i−i−i−i−iiiiiii−i−i-1-111
χ91111-111-1-11111-1-1-1111111-11111-1-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-11-11-111-1-111-1-11-11-11-11-1
χ101111-111-1-11111-1-1-1111111-11111-1-1-1-1-1-1-1-1-11111-1-11111-1111-1-1-1-1-1-11-1111-1-111-1-1-11-11-11-11
χ111111-111-1-11111-1-1-1111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1-111-11-11-1-111-1-111-11-111-11-1
χ121111-111-1-11111-1-1-1111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1111-11-1-1-111-1-1111-11-1-11-11
χ131111-111-1-11111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i1-1-1-1111−iii−i−iiii−i−i−i−iiii−i−ii1-1-11
χ141111-111-1-11111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i-11-1-1111−ii−iii−iii−i−i−i−iii−iii−i-111-1
χ151111-111-1-11111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11-1-1-1-111−i−iii1-1-1-1111i−i−iii−i−i−iiiii−i−i−iii−i1-1-11
χ161111-111-1-11111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11-1-1-1-111−i−iii-11-1-1111i−ii−i−ii−i−iiiii−i−ii−i−ii-111-1
χ17222-122-122-12-12-1-1-1222-1-1-122-1-1-122-1-1-1-1-1-12-122-122000000-1-1-1-1-100222200000000-1-1-1-10000
χ18222-122-122-12-12-1-1-1222-1-1-122-1-1-122-1-1-1-1-1-12-122-122000000-1-1-1-1-100-2-2-2-20000000011110000
χ19222-122-122-12-12-1-1-1-2-22-1-1-122-1-1-122-1-1-1-1-1-1-21-2-21-2-200000011111002i2i−2i−2i00000000−i−iii0000
χ20222-122-122-12-12-1-1-1-2-22-1-1-122-1-1-122-1-1-1-1-1-1-21-2-21-2-20000001111100−2i−2i2i2i00000000ii−i−i0000
χ21222-1-22-1-2-2-12-12111222-1-1-1-22-1-1-1-2-2111111-2-122-1-2-2000000-1-1111002-22-200000000-11-110000
χ22222-1-22-1-2-2-12-12111222-1-1-1-22-1-1-1-2-2111111-2-122-1-2-2000000-1-111100-22-22000000001-11-10000
χ23222-1-22-1-2-2-12-12111-2-22-1-1-1-22-1-1-1-2-211111121-2-212200000011-1-1-1002i−2i−2i2i00000000−iii−i0000
χ24222-1-22-1-2-2-12-12111-2-22-1-1-1-22-1-1-1-2-211111121-2-212200000011-1-1-100−2i2i2i−2i00000000i−i−ii0000
χ2522-122-12-1-1-12-122-1-122-12-1-12-12-1-1-1-122-1-1-1-122-1-12-1-1222200-1-12-1-1220000-1-1-1-1-1-1-1-100000000
χ2622-122-12-1-1-12-122-1-122-12-1-12-12-1-1-1-122-1-1-1-122-1-12-1-1-2-2-2-200-1-12-1-1-2-200001111111100000000
χ2722-122-12-1-1-12-122-1-1-2-2-12-1-12-12-1-1-1-122-1-1-1-1-2-211-2112i2i−2i−2i0011-2112i−2i0000−i−i−i−iiiii00000000
χ2822-122-12-1-1-12-122-1-1-2-2-12-1-12-12-1-1-1-122-1-1-1-1-2-211-211−2i−2i2i2i0011-211−2i2i0000iiii−i−i−i−i00000000
χ2922-12-2-1211-12-12-21122-12-1-1-2-12-1-111-2-21111-22-1-1211222200-1-1-211-2-20000-1-111-1-11100000000
χ3022-12-2-1211-12-12-21122-12-1-1-2-12-1-111-2-21111-22-1-1211-2-2-2-200-1-1-21122000011-1-111-1-100000000
χ3122-12-2-1211-12-12-211-2-2-12-1-1-2-12-1-111-2-211112-211-2-1-12i2i−2i−2i00112-1-1−2i2i0000−i−iiiii−i−i00000000
χ3222-12-2-1211-12-12-211-2-2-12-1-1-2-12-1-111-2-211112-211-2-1-1−2i−2i2i2i00112-1-12i−2i0000ii−i−i−i−iii00000000
χ332-2220-2-20022-2-20002-222220-2-2-2-200000000022-2-2002i−2i2i−2i002-20000000002i−2i002i−2i0000000000
χ342-2220-2-20022-2-20002-222220-2-2-2-200000000022-2-200−2i2i−2i2i002-2000000000−2i2i00−2i2i0000000000
χ352-2220-2-20022-2-2000-2222220-2-2-2-2000000000-2-222002-2-2200-220000000002-200-220000000000
χ362-2220-2-20022-2-2000-2222220-2-2-2-2000000000-2-22200-222-200-22000000000-22002-20000000000
χ372-2-1201-23−3-121-203−32-2-12-1-101-2113−30033−3−302-11-23−32i−2i2i−2i00-1103−3000000−ii−i3i3−ii−i3i300000000
χ382-2-1201-23−3-121-203−32-2-12-1-101-2113−30033−3−302-11-23−3−2i2i−2i2i00-1103−3000000i−ii3−i3i−ii3−i300000000
χ392-2-1201-23−3-121-203−3-22-12-1-101-2113−30033−3−30-21-12−332-2-22001-10−33000000-11−331-13−300000000
χ402-2-1201-23−3-121-203−3-22-12-1-101-2113−30033−3−30-21-12−33-222-2001-10−330000001-13−3-11−3300000000
χ412-2-1201-2−33-121-20−332-2-12-1-101-211−3300−3−33302-11-2−332i−2i2i−2i00-110−33000000−iii3−i3−iii3−i300000000
χ422-2-1201-2−33-121-20−332-2-12-1-101-211−3300−3−33302-11-2−33−2i2i−2i2i00-110−33000000i−i−i3i3i−i−i3i300000000
χ432-2-1201-2−33-121-20−33-22-12-1-101-211−3300−3−3330-21-123−32-2-22001-103−3000000-113−31-1−3300000000
χ442-2-1201-2−33-121-20−33-22-12-1-101-211−3300−3−3330-21-123−3-222-2001-103−30000001-1−33-113−300000000
χ454444444444-14-144400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000004400000000000000000000000-1-100
χ464444444444-14-144400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000-4-4000000000000000000000001100
χ474444-444-4-44-14-1-4-4-400-1-1-1-11-1-1-1-111111111000000000004-400000000000000000000000-1100
χ484444-444-4-44-14-1-4-4-400-1-1-1-11-1-1-1-11111111100000000000-44000000000000000000000001-100
χ4944-2-24-2-2-2-21414-21144-2-2114-2-211-2-2-2-211114-2-2-2-2-2-200000011-2110000000000000000000000
χ5044-2-24-2-2-2-21414-211-4-4-2-2114-2-211-2-2-2-21111-4222222000000-1-12-1-10000000000000000000000
χ5144-2-2-4-2-22214142-1-144-2-211-4-2-2112222-1-1-1-1-4-2-2-2-222000000112-1-10000000000000000000000
χ5244-2-2-4-2-22214142-1-1-4-4-2-211-4-2-2112222-1-1-1-142222-2-2000000-1-1-2110000000000000000000000
χ534-44-20-4200-242-40004-44-2-2-20-4222000000000-24-4200000000-220000000000000000000000000
χ544-44-20-4200-242-4000-444-2-2-20-42220000000002-44-2000000002-20000000000000000000000000
χ554-4-2-202223−2314-1-40−334-4-2-211022-1-123−2300−3−3330-2-22223−230000001-10−330000000000000000000000
χ564-4-2-202223−2314-1-40−33-44-2-211022-1-123−2300−3−333022-2-2−2323000000-1103−30000000000000000000000
χ574-4-2-2022−232314-1-403−34-4-2-211022-1-1−23230033−3−30-2-222−23230000001-103−30000000000000000000000
χ584-4-2-2022−232314-1-403−3-44-2-211022-1-1−23230033−3−3022-2-223−23000000-110−330000000000000000000000
χ59888-488-488-4-2-4-2-4-4-400-2111-2-2111-2-21111110000000000000000000000000000000000000000
χ60888-4-88-4-8-8-4-2-4-244400-21112-211122-1-1-1-1-1-10000000000000000000000000000000000000000
χ6188-488-48-4-4-4-2-4-28-4-4001-211-21-21111-2-211110000000000000000000000000000000000000000
χ6288-48-8-4844-4-2-4-2-844001-21121-211-1-122-1-1-1-10000000000000000000000000000000000000000
χ6388-4-48-4-4-4-42-22-2-4220011−1−352−1+352-211−1−352−1+3521111−1−352−1+352−1−352−1+3520000000000000000000000000000000000000000
χ6488-4-48-4-4-4-42-22-2-4220011−1+352−1−352-211−1+352−1−3521111−1+352−1−352−1+352−1−3520000000000000000000000000000000000000000
χ6588-4-4-8-4-4442-22-24-2-20011−1−352−1+352211−1−352−1+352-1-1-1-11+3521−3521+3521−3520000000000000000000000000000000000000000
χ6688-4-4-8-4-4442-22-24-2-20011−1+352−1−352211−1+352−1−352-1-1-1-11−3521+3521−3521+3520000000000000000000000000000000000000000
χ678-8880-8-8008-2-8200000-2-2-2-202222000000000000000000000000000000000000000000000000
χ688-88-40-8400-4-24200000-211102-1-1-100−1515−151515−150000000000000000000000000000000000000000
χ698-88-40-8400-4-24200000-211102-1-1-10015−1515−15−15150000000000000000000000000000000000000000
χ708-8-4804-843−43-4-242043−43001-2110-12-1-1−3300−3−3330000000000000000000000000000000000000000
χ718-8-4804-8−4343-4-2420−4343001-2110-12-1-13−30033−3−30000000000000000000000000000000000000000
χ728-8-4-404443−432-2-220−23230011−1−352−1+3520-1-11+3521−352−3315−15−ζ7+ζ23−ζ43+ζ47ζ11−ζ19−ζ31+ζ59ζ7−ζ23+ζ43−ζ47−ζ11+ζ19+ζ31−ζ590000000000000000000000000000000000000000
χ738-8-4-404443−432-2-220−23230011−1+352−1−3520-1-11−3521+352−33−1515ζ11−ζ19−ζ31+ζ59−ζ7+ζ23−ζ43+ζ47−ζ11+ζ19+ζ31−ζ59ζ7−ζ23+ζ43−ζ470000000000000000000000000000000000000000
χ748-8-4-4044−43432-2-22023−230011−1−352−1+3520-1-11+3521−3523−3−1515ζ7−ζ23+ζ43−ζ47−ζ11+ζ19+ζ31−ζ59−ζ7+ζ23−ζ43+ζ47ζ11−ζ19−ζ31+ζ590000000000000000000000000000000000000000
χ758-8-4-4044−43432-2-22023−230011−1+352−1−3520-1-11−3521+3523−315−15−ζ11+ζ19+ζ31−ζ59ζ7−ζ23+ζ43−ζ47ζ11−ζ19−ζ31+ζ59−ζ7+ζ23−ζ43+ζ470000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.