Finite Group Databasebeta

← Group #72230806

Character table — Group #72230806

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122244444888888888812161616161616161616161616202025253030303040404848484848485050505050505075757575808080808080100100100100100100100120120120120150150200200300300300
order123465510101255101015152020303021515202030306060606060604422888812121010101010104668888444420206060606044122424242440404040441212244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1-1-11-1-1
χ31111111111111111111111111111111111-1-1-111-1-11-1111111-1-1-1ii−i−iii−i−i1-111-1-1i−i-1ii−i−i11-1-1i−ii−i-1i−i
χ41111111111111111111111111111111111-1-1-111-1-11-1111111-1-1-1−i−iii−i−iii1-111-1-1−ii-1−i−iii11-1-1−ii−ii-1−ii
χ5111111111111111111111111111111111-11-1-1-1-111-11111111-1-1-1ii−i−i−i−iii-11-1-111−ii-1ii−i−i-1-111−ii−ii-1i−i
χ6111111111111111111111111111111111-11-1-1-1-111-11111111-1-1-1−i−iiiii−i−i-11-1-111i−i-1−i−iii-1-111i−ii−i-1−ii
χ7111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111
χ8111111111111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1
χ911111111111111111111-11111111111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1
χ1011111111111111111111-11111111111111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-111-1-1-111
χ1111111111111111111111-11111111111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1-111-1-1i−i-1ii−i−i-1-111−iii−i1−ii
χ1211111111111111111111-11111111111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1-111-1-1−ii-1−i−iii-1-111i−i−ii1i−i
χ1311111111111111111111-1111111111111-11-1-111-1-1-11-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-11-1-111−ii-1ii−i−i11-1-1i−i−ii1−ii
χ1411111111111111111111-1111111111111-11-1-111-1-1-11-1-1-1-1-1-1-1-1-1−i−iii−i−iii-11-1-111i−i-1−i−iii11-1-1−iii−i1i−i
χ1511111111111111111111-1111111111111-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1
χ1611111111111111111111-1111111111111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-111-111
χ17222-222222-2222222-2-222022-2-222-2-2-2-2-2-20022000000000000-2220000222200000000-200000000-2-200000
χ18222-222222-2222222-2-222022-2-222-2-2-2-2-2-20022000000000000-2220000-2-2-2-200000000-2000000002200000
χ19222-222222-2222222-2-222022-2-222-2-2-2-2-2-200-2-20000000000002-2-200002i2i−2i−2i00000000200000000−2i2i00000
χ20222-222222-2222222-2-222022-2-222-2-2-2-2-2-200-2-20000000000002-2-20000−2i−2i2i2i000000002000000002i−2i00000
χ2122-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-122220000-1-10000002-1-12222000022-1-1-1-122-1-1-1-1-1000000-1-1000
χ2222-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-122220000-1-10000002-1-1-2-2-2-2000022-1-1-1-1-2-2-1111100000011000
χ2322-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-12-2-2-20000-11000000-2112i2i−2i−2i00002-2-1-1112i−2i1−i−iii000000−ii000
χ2422-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-12-2-2-20000-11000000-211−2i−2i2i2i00002-2-1-111−2i2i1ii−i−i000000i−i000
χ2522-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-1-22-2-200001-1000000-2112i2i−2i−2i0000-2211-1-1−2i2i1−i−iii000000i−i000
χ2622-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-1-22-2-200001-1000000-211−2i−2i2i2i0000-2211-1-12i−2i1ii−i−i000000−ii000
χ2722-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-1-2-2220000110000002-1-122220000-2-21111-2-2-1-1-1-1-100000011000
χ2822-12-12222-12222-1-122-1-10-1-122-1-1-1-1-1-1-1-1-2-2220000110000002-1-1-2-2-2-20000-2-2111122-11111000000-1-1000
χ292-220-222-2-2022-2-22200-2-202200-2-2000000002-2−i2i2−i2i2000000000-22−i2i2−i2i22-22-2000000000−i2i2−i2i2−i2i2−i2i20000000
χ302-220-222-2-2022-2-22200-2-202200-2-2000000002-2−i2i2−i2i2000000000-22i2−i2i2−i2-22-22000000000i2−i2i2−i2−i2i2−i2i20000000
χ312-220-222-2-2022-2-22200-2-202200-2-2000000002-2i2−i2i2−i2000000000-22−i2i2−i2i2-22-22000000000−i2i2−i2i2i2−i2i2−i20000000
χ322-220-222-2-2022-2-22200-2-202200-2-2000000002-2i2−i2i2−i2000000000-22i2−i2i2−i22-22-2000000000i2−i2i2−i2i2−i2i2−i20000000
χ332-220-222-2-2022-2-22200-2-202200-2-200000000-22−i2i2i2−i20000000002-22−2−222i−2i−2i2i0000000002−2−22−i2i2i2−i20000000
χ342-220-222-2-2022-2-22200-2-202200-2-200000000-22−i2i2i2−i20000000002-2−222−2−2i2i2i−2i000000000−222−2−i2i2i2−i20000000
χ352-220-222-2-2022-2-22200-2-202200-2-200000000-22i2−i2−i2i20000000002-22−2−22−2i2i2i−2i0000000002−2−22i2−i2−i2i20000000
χ362-220-222-2-2022-2-22200-2-202200-2-200000000-22i2−i2−i2i20000000002-2−222−22i−2i−2i2i000000000−222−2i2−i2−i2i20000000
χ37444444-14-14-1-1-1-14-14-14-14-1-1-1-1-1-14-1-1-1-1-104000044044-1-1-1-1-1000000000000-100-1-1000000000-1-10000000
χ38444444-14-14-1-1-1-14-14-14-14-1-1-1-1-1-14-1-1-1-1-10-40000-4-40-44-1-1-1-1-100000000000010011000000000110000000
χ39444444-14-14-1-1-1-14-14-14-1-4-1-1-1-1-1-14-1-1-1-1-1040000-4-404-411111000000000000-100-1-1000000000110000000
χ40444444-14-14-1-1-1-14-14-14-1-4-1-1-1-1-1-14-1-1-1-1-10-40000440-4-41111100000000000010011000000000-1-10000000
χ4144444-14-144-1-1-1-1-14-14-144-1-1-1-1-1-1-14-1-1-1-14000440040-14-1-1-1-100000000000-10-1-1000000000-1-1000000000
χ4244444-14-144-1-1-1-1-14-14-144-1-1-1-1-1-1-14-1-1-1-1-4000-4-400-40-14-1-1-1-100000000000101100000000011000000000
χ4344444-14-144-1-1-1-1-14-14-14-4-1-1-1-1-1-1-14-1-1-1-14000-4-400401-4111100000000000-10-1-100000000011000000000
χ4444444-14-144-1-1-1-1-14-14-14-4-1-1-1-1-1-1-14-1-1-1-1-40004400-401-41111000000000001011000000000-1-1000000000
χ4544-2-4-2444424444-2-2-4-4-2-20-2-2-4-4-2-22222220044000000000000-4-2-200000000000000002000000000000000
χ4644-2-4-2444424444-2-2-4-4-2-20-2-2-4-4-2-222222200-4-40000000000004220000000000000000-2000000000000000
χ474-4-20244-4-4044-4-4-2-200220-2-20022000000004-400000000000002-2−2i22i2−2i22i20000000000000i2−i2i2−i200000000000
χ484-4-20244-4-4044-4-4-2-200220-2-20022000000004-400000000000002-22i2−2i22i2−2i20000000000000−i2i2−i2i200000000000
χ494-4-20244-4-4044-4-4-2-200220-2-2002200000000-440000000000000-2222−22−22220000000000000−222−200000000000
χ504-4-20244-4-4044-4-4-2-200220-2-2002200000000-440000000000000-22−222222−2200000000000002−2−2200000000000
χ5188888-2-2-2-283-23-2-2-2-2-2-2-283-23-23-2-2-233-2-20000000000-2-233-2-200000000000000000000000000000000000
χ5288888-2-2-2-283-23-2-2-2-2-2-2-2-83-23-23-2-2-233-2-2000000000022-3-32200000000000000000000000000000000000
χ5388888-2-2-2-28-23-23-2-2-2-2-2-28-23-23-23-2-2-2-2330000000000-2-2-2-23300000000000000000000000000000000000
χ5488888-2-2-2-28-23-23-2-2-2-2-2-2-8-23-23-23-2-2-2-23300000000002222-3-300000000000000000000000000000000000
χ55888-888-28-2-8-2-2-2-28-2-828-20-2-222-2-2-822222000000000000000000000000000000000000000000000000000
χ56888-88-28-28-8-2-2-2-2-282-8-280-2-222-2-22-82222000000000000000000000000000000000000000000000000000
χ57888-88-2-2-2-2-83-23-2-2-222-2-203-2-323-222-3-3220000000000005-50000000000000000000000000000000000000
χ58888-88-2-2-2-2-83-23-2-2-222-2-203-2-323-222-3-322000000000000-550000000000000000000000000000000000000
χ59888-88-2-2-2-2-8-23-23-2-222-2-20-232-3-232222-3-3000000000000005-500000000000000000000000000000000000
χ60888-88-2-2-2-2-8-23-23-2-222-2-20-232-3-232222-3-300000000000000-5500000000000000000000000000000000000
χ6188-48-48-28-2-4-2-2-2-2-418-2-41011-2-211-411111080000000-4000000000000000000-20011000000000000000000
χ6288-48-48-28-2-4-2-2-2-2-418-2-41011-2-211-4111110-800000004000000000000000000200-1-1000000000000000000
χ6388-48-4-28-28-4-2-2-2-21-4-281-4011-2-2111-4111180000000-4000000000000000000-201100000000000000000000
χ6488-48-4-28-28-4-2-2-2-21-4-281-4011-2-2111-41111-80000000400000000000000000020-1-100000000000000000000
χ6588-4-8-48-28-24-2-2-2-2-41-82-4101122114-1-1-1-1-10000000000000000000000000000000−i15i15000000000000000000
χ6688-4-8-48-28-24-2-2-2-2-41-82-4101122114-1-1-1-1-10000000000000000000000000000000i15−i15000000000000000000
χ6788-4-8-4-28-284-2-2-2-21-42-81-40112211-14-1-1-1-100000000000000000000000000000−i15i1500000000000000000000
χ6888-4-8-4-28-284-2-2-2-21-42-81-40112211-14-1-1-1-100000000000000000000000000000i15−i1500000000000000000000
χ698-880-88-2-820-2-2228-200-820-2-20022000000000000−4i24i20000000000000000000000000000000000i2−i20000000
χ708-880-88-2-820-2-2228-200-820-2-200220000000000004i2−4i20000000000000000000000000000000000−i2i20000000
χ718-880-8-282-80-2-222-28002-80-2-200220000000000−4i24i20000000000000000000000000000000000i2−i2000000000
χ728-880-8-282-80-2-222-28002-80-2-2002200000000004i2−4i20000000000000000000000000000000000−i2i2000000000
χ731616-816-8-4-4-4-4-86-46-422-4-4220-326-4-3222-3-322000000000000000000000000000000000000000000000000000
χ741616-816-8-4-4-4-4-8-46-4622-4-42202-3-462-32222-3-3000000000000000000000000000000000000000000000000000
χ751616-8-16-8-4-4-4-486-46-42244220-32-64-32-2-233-2-2000000000000000000000000000000000000000000000000000
χ761616-8-16-8-4-4-4-48-46-4622442202-34-62-3-2-2-2-233000000000000000000000000000000000000000000000000000
χ7716-16160-16-4-44406-4-64-4-4004406-400-64000000000000000000000000000000000000000000000000000000000
χ7816-16160-16-4-4440-464-6-4-400440-46004-6000000000000000000000000000000000000000000000000000000000
χ7916-16-80816-4-1640-4-444-82008-202200-2-2000000000000000000000000000000000000000000000000000000000
χ8016-16-808-4164-160-4-4442-800-2802200-2-2000000000000000000000000000000000000000000000000000000000
χ8116-16-808-4-44406-4-642200-2-20-32003-200−1515−215215000000000000000000000000000000000000000000000000000
χ8216-16-808-4-44406-4-642200-2-20-32003-20015−15215−215000000000000000000000000000000000000000000000000000
χ8316-16-808-4-4440-464-62200-2-202-300-2300−21521515−15000000000000000000000000000000000000000000000000000
χ8416-16-808-4-4440-464-62200-2-202-300-2300215−215−1515000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).