Finite Group Databasebeta

← Group #72231097

Character table — Group #72231097

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222224444888888888888888888888888888888888825252525252530303030505050505050505050505050505050120120120120150150150150
order1223666551010551010101010101010151515151515303030303030303030303030303030303030224444224424466661212121212121212101020204444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111111-1-1ii−i−i1-11-1-1i−i-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i
χ6111111111111111111111111111111111111111111111-1-1ii−i−i-11-11-1i−i-1-1-1-1iiii−i−i−i−i-11-11−ii−ii
χ7111111111111111111111111111111111111111111111-1-1−i−iii1-11-1-1−ii-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii
χ8111111111111111111111111111111111111111111111-1-1−i−iii-11-11-1−ii-1-1-1-1−i−i−i−iiiii-11-11i−ii−i
χ911-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111
χ1011-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-1111-1-111-1-1-1-11111-1-1
χ1111-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-11-1-111-1-11111-1-111-1-1
χ1211-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-11-1-111-1-111-1-111-1-111
χ1311-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1-1-111−ii-111-1ii−i−i−i−iii1-1-11−iii−i
χ1411-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-111-11−ii-111-1ii−i−i−i−iii-111-1i−i−ii
χ1511-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1-1-111i−i-111-1−i−iiiii−i−i1-1-11i−i−ii
χ1611-111-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-111-11i−i-111-1−i−iiiii−i−i-111-1−iii−i
χ17222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222220000222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-200002-2-2-1-1-1-11111111100000000
χ19222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22i2i−2i−2i0000-22i−2i1111−i−i−i−iiiii00000000
χ20222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2−2i−2i2i2i0000-2−2i2i1111iiii−i−i−i−i00000000
χ2122-2-1-111222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111112222220000-2-2-2-111-1-1-111-1-11100000000
χ2222-2-1-111222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-2-2-20000-222-111-111-1-111-1-100000000
χ2322-2-1-111222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-22i2i−2i−2i00002−2i2i1-1-11−i−iiiii−i−i00000000
χ2422-2-1-111222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-2−2i−2i2i2i000022i−2i1-1-11ii−i−i−i−iii00000000
χ252-202-20022-2-22200-2-20000222222-2-2-2-2-2-20000000000002-22i−2i2i−2i0000000200-22i−2i002i−2i0000000000
χ262-202-20022-2-22200-2-20000222222-2-2-2-2-2-20000000000002-2−2i2i−2i2i0000000200-2−2i2i00−2i2i0000000000
χ272-202-20022-2-22200-2-20000222222-2-2-2-2-2-2000000000000-222-2-220000000-20022-200-220000000000
χ282-202-20022-2-22200-2-20000222222-2-2-2-2-2-2000000000000-22-222-20000000-2002-22002-20000000000
χ292-20-11−i3i322-2-22200-2-20000-1-1-1-1-1-1111111−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-22i−2i2i−2i0000000-1−i3i31−ii3−3−ii3−300000000
χ302-20-11−i3i322-2-22200-2-20000-1-1-1-1-1-1111111−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-2−2i2i−2i2i0000000-1−i3i31i−i−33i−i−3300000000
χ312-20-11−i3i322-2-22200-2-20000-1-1-1-1-1-1111111−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-222-2-2200000001i3−i3-1-11−i3i31-1i3−i300000000
χ322-20-11−i3i322-2-22200-2-20000-1-1-1-1-1-1111111−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-22-222-200000001i3−i3-11-1i3−i3-11−i3i300000000
χ332-20-11i3−i322-2-22200-2-20000-1-1-1-1-1-1111111i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-22i−2i2i−2i0000000-1i3−i31−ii−33−ii−3300000000
χ342-20-11i3−i322-2-22200-2-20000-1-1-1-1-1-1111111i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-2−2i2i−2i2i0000000-1i3−i31i−i3−3i−i3−300000000
χ352-20-11i3−i322-2-22200-2-20000-1-1-1-1-1-1111111i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-222-2-2200000001−i3i3-1-11i3−i31-1−i3i300000000
χ362-20-11i3−i322-2-22200-2-20000-1-1-1-1-1-1111111i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-22-222-200000001−i3i3-11-1−i3i3-11i3−i300000000
χ3744444444-14-1-1-14-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-100000004040000000000000000-10-10000
χ3844444444-14-1-1-14-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-10000000-40-400000000000000001010000
χ394444444-14-14-1-1-14-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-10000004040000000000000000-10-100000
χ404444444-14-14-1-1-14-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1000000-40-4000000000000000010100000
χ4144-444-4-44-14-1-1-1-41-1-111114-1-1-1-1-14-1-1-1-1-1-411111-411111000000040-40000000000000000-1010000
χ4244-444-4-44-14-1-1-1-41-1-111114-1-1-1-1-14-1-1-1-1-1-411111-4111110000000-404000000000000000010-10000
χ4344-444-4-4-14-14-1-11-4-1-11111-14-1-1-1-1-14-1-1-1-11-411111-4111100000040-40000000000000000-10100000
χ4444-444-4-4-14-14-1-11-4-1-11111-14-1-1-1-1-14-1-1-1-11-411111-41111000000-404000000000000000010-100000
χ458888888-2-2-2-23-2-2-23-233-2-2-2-233-2-2-2-233-2-2-2-233-2-2-2-233-2-2000000000000000000000000000000000
χ468888888-2-2-2-2-23-2-2-23-2-233-2-2-2-233-2-2-2-233-2-2-2-233-2-2-2-233000000000000000000000000000000000
χ47888-4-4-4-48-28-2-2-28-2-2-2-2-2-2-2-411111-411111-411111-411111000000000000000000000000000000000
χ48888-4-4-4-4-28-28-2-2-28-2-2-2-2-2-21-411111-411111-411111-41111000000000000000000000000000000000
χ49888-4-4-4-4-2-2-2-23-2-2-23-233-2-211−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i15000000000000000000000000000000000
χ50888-4-4-4-4-2-2-2-23-2-2-23-233-2-211−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i15000000000000000000000000000000000
χ51888-4-4-4-4-2-2-2-2-23-2-2-23-2-233111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i152000000000000000000000000000000000
χ52888-4-4-4-4-2-2-2-2-23-2-2-23-2-233111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i152000000000000000000000000000000000
χ5388-888-8-8-2-2-2-23-2223-2-3-322-2-233-2-2-2-233-2-222-3-32222-3-322000000000000000000000000000000000
χ5488-888-8-8-2-2-2-2-2322-2322-3-3-2-2-2-233-2-2-2-2332222-3-32222-3-3000000000000000000000000000000000
χ5588-8-4-4448-28-2-2-2-82-2-22222-411111-4111114-1-1-1-1-14-1-1-1-1-1000000000000000000000000000000000
χ5688-8-4-444-28-28-2-22-8-2-222221-411111-41111-14-1-1-1-1-14-1-1-1-1000000000000000000000000000000000
χ5788-8-4-444-2-2-2-23-2223-2-3-32211−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i15-1-13+i1523−i152−1+i15−1−i15000000000000000000000000000000000
χ5888-8-4-444-2-2-2-23-2223-2-3-32211−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i15-1-13−i1523+i152−1−i15−1+i15000000000000000000000000000000000
χ5988-8-4-444-2-2-2-2-2322-2322-3-3111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i152-1-1−1+i15−1−i153−i1523+i152000000000000000000000000000000000
χ6088-8-4-444-2-2-2-2-2322-2322-3-3111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i152-1-1−1−i15−1+i153+i1523−i152000000000000000000000000000000000
χ618-808-8008-2-82-2-2002200008-2-2-2-2-2-822222000000000000000000000000000000000000000000000
χ628-808-800-282-8-2-200220000-28-2-2-2-22-82222000000000000000000000000000000000000000000000
χ638-808-800-2-2223-200-32−55−2525-2-233-2-222-3-32200−55−2525005−525−25000000000000000000000000000000000
χ648-808-800-2-2223-200-325−525−25-2-233-2-222-3-322005−525−2500−55−2525000000000000000000000000000000000
χ658-808-800-2-222-23002-3−25255−5-2-2-2-2332222-3-300−25255−50025−25−55000000000000000000000000000000000
χ668-808-800-2-222-23002-325−25−55-2-2-2-2332222-3-30025−25−5500−25255−5000000000000000000000000000000000
χ678-80-44−4i34i38-2-82-2-200220000-4111114-1-1-1-1-1−4i3i3i3i3i3i34i3−i3−i3−i3−i3−i3000000000000000000000000000000000
χ688-80-44−4i34i3-282-8-2-2002200001-41111-14-1-1-1-1i3−4i3i3i3i3i3−i34i3−i3−i3−i3−i3000000000000000000000000000000000
χ698-80-44−4i34i3-2-2223-200-32−55−252511−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i15i3i3−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ582ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−i3−i3ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ58000000000000000000000000000000000
χ708-80-44−4i34i3-2-2223-200-325−525−2511−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i15i3i3−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ582ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−i3−i32ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ46000000000000000000000000000000000
χ718-80-44−4i34i3-2-222-23002-3−25255−5111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i152i3i32ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58−i3−i3−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ58000000000000000000000000000000000
χ728-80-44−4i34i3-2-222-23002-325−25−55111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i152i3i32ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58−i3−i3−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ46ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58000000000000000000000000000000000
χ738-80-444i3−4i38-2-82-2-200220000-4111114-1-1-1-1-14i3−i3−i3−i3−i3−i3−4i3i3i3i3i3i3000000000000000000000000000000000
χ748-80-444i3−4i3-282-8-2-2002200001-41111-14-1-1-1-1−i34i3−i3−i3−i3−i3i3−4i3i3i3i3i3000000000000000000000000000000000
χ758-80-444i3−4i3-2-2223-200-32−55−252511−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i15−i3−i32ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ46i3i3−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ582ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46000000000000000000000000000000000
χ768-80-444i3−4i3-2-2223-200-325−525−2511−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i15−i3−i3ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ58i3i3−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ582ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58000000000000000000000000000000000
χ778-80-444i3−4i3-2-222-23002-3−25255−5111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i152−i3−i3−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ46ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58i3i32ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58000000000000000000000000000000000
χ788-80-444i3−4i3-2-222-23002-325−25−55111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i152−i3−i3−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ2+ζ14−ζ22+ζ26−2ζ34+2ζ38−2ζ46−ζ58ζ2+2ζ14−2ζ22+2ζ26−ζ34+ζ38−ζ46−2ζ58i3i32ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ2−ζ14+ζ22−ζ26+2ζ34−2ζ38+2ζ46+ζ58−ζ2−2ζ14+2ζ22−2ζ26+ζ34−ζ38+ζ46+2ζ58000000000000000000000000000000000

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