Finite Group Databasebeta

← Group #72231029

Character table — Group #72231029

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11224444555568888888810101010121212121616161620202020242424242525303040404040505050505050505050505050505060606060150150150150150
order12365510104444255101015153030121212121010101015153030202020201010101022446060606044446612121212121212122020202024444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1
χ3111111111111-1111111111111-1-1-1-111111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ4111111111111-1111111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111111111111-1-11111111111-1-11111-1-11-111-1-1ii−i−i-1-1iiii−i−i−i−i11-1-1-1ii−i−i
χ61111111111-1-111111111111-1-11111111111-1-11111-1-11-111-1-1−i−iii-1-1−i−i−i−iiiii11-1-1-1−i−iii
χ71111111111-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1111−i−iii
χ81111111111-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1−i−iii-1-1−i−i−i−iiiii-1-1111ii−i−i
χ911111111-1-111111111111-1-11111111111-1-1111111-1-1-11-1-111i−ii−i-1-1ii−i−iii−i−i-1-111-1i−ii−i
χ1011111111-1-111111111111-1-11111111111-1-1111111-1-1-11-1-111−ii−ii-1-1−i−iii−i−iii-1-111-1−ii−ii
χ1111111111-1-111-111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11-1-1-111i−ii−i-1-1ii−i−iii−i−i11-1-11−ii−ii
χ1211111111-1-111-111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11-1-1-111−ii−ii-1-1−i−iii−i−iii11-1-11i−ii−i
χ1311111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-111-1-11
χ1411111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-11-111-1
χ1511111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1
χ1611111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-11111-1-11111-11-1-11
χ1722-1-12222222202222-1-1-1-1-1-1-1-10000-1-1-1-1222200002200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000000
χ1822-1-12222222202222-1-1-1-1-1-1-1-10000-1-1-1-1222200002200-1-1-1-1-2-2-2-2-1-111111111000000000
χ1922-1-1222222-2-202222-1-1-1-1-1-1110000-1-1-1-122-2-20000-2-200-1-1112i2i−2i−2i11−i−i−i−iiiii000000000
χ2022-1-1222222-2-202222-1-1-1-1-1-1110000-1-1-1-122-2-20000-2-200-1-111−2i−2i2i2i11iiii−i−i−i−i000000000
χ2122-1-12222-2-22202222-1-1-1-111-1-10000-1-1-1-1-2-2220000-2-20011-1-12i−2i2i−2i11−i−iii−i−iii000000000
χ2222-1-12222-2-22202222-1-1-1-111-1-10000-1-1-1-1-2-2220000-2-20011-1-1−2i2i−2i2i11ii−i−iii−i−i000000000
χ2322-1-12222-2-2-2-202222-1-1-1-111110000-1-1-1-1-2-2-2-20000220011112-2-22-1-1-1-11111-1-1000000000
χ2422-1-12222-2-2-2-202222-1-1-1-111110000-1-1-1-1-2-2-2-2000022001111-222-2-1-111-1-1-1-111000000000
χ252-22-222-2-22i−2i2i−2i022-2-222-2-22i−2i2i−2i000022-2-22i−2i2i−2i00002-2002i−2i2i−2i00002-200000000000000000
χ262-22-222-2-22i−2i−2i2i022-2-222-2-22i−2i−2i2i000022-2-22i−2i−2i2i0000-22002i−2i−2i2i0000-2200000000000000000
χ272-22-222-2-2−2i2i2i−2i022-2-222-2-2−2i2i2i−2i000022-2-2−2i2i2i−2i0000-2200−2i2i2i−2i0000-2200000000000000000
χ282-22-222-2-2−2i2i−2i2i022-2-222-2-2−2i2i−2i2i000022-2-2−2i2i−2i2i00002-200−2i2i−2i2i00002-200000000000000000
χ292-2-1122-2-22i−2i2i−2i022-2-2-1-111−ii−ii0000-1-1112i−2i2i−2i00002-200−ii−ii0000-11−i3i33−33−3−i3i3000000000
χ302-2-1122-2-22i−2i2i−2i022-2-2-1-111−ii−ii0000-1-1112i−2i2i−2i00002-200−ii−ii0000-11i3−i3−33−33i3−i3000000000
χ312-2-1122-2-22i−2i−2i2i022-2-2-1-111−iii−i0000-1-1112i−2i−2i2i0000-2200−iii−i00001-13−3i3−i3−i3i3−33000000000
χ322-2-1122-2-22i−2i−2i2i022-2-2-1-111−iii−i0000-1-1112i−2i−2i2i0000-2200−iii−i00001-1−33−i3i3i3−i33−3000000000
χ332-2-1122-2-2−2i2i2i−2i022-2-2-1-111i−i−ii0000-1-111−2i2i2i−2i0000-2200i−i−ii00001-13−3−i3i3i3−i3−33000000000
χ342-2-1122-2-2−2i2i2i−2i022-2-2-1-111i−i−ii0000-1-111−2i2i2i−2i0000-2200i−i−ii00001-1−33i3−i3−i3i33−3000000000
χ352-2-1122-2-2−2i2i−2i2i022-2-2-1-111i−ii−i0000-1-111−2i2i−2i2i00002-200i−ii−i0000-11−i3i3−33−33−i3i3000000000
χ362-2-1122-2-2−2i2i−2i2i022-2-2-1-111i−ii−i0000-1-111−2i2i−2i2i00002-200i−ii−i0000-11i3−i33−33−3i3−i3000000000
χ3744444-14-100444-1-1-1-14-14-1004444-1-1-1-1-1-100-1-1-1-1-1-1000400-1-10000000000000000-1-100000
χ3844444-14-10044-4-1-1-1-14-14-10044-4-411-1-1-1-100-1-11111000-400-1-100000000000000001100000
χ3944444-14-100-4-44-1-1-1-14-14-100-4-444-1-1-1-1-1-10011-1-1-1-1000-4001100000000000000001100000
χ4044444-14-100-4-4-4-1-1-1-14-14-100-4-4-4-411-1-1-1-100111111000400110000000000000000-1-100000
χ414444-14-1444004-1-1-1-1-14-144400-1-144-1-1-1-1-1-100-1-1-1-10040-1-10000000000000000-1-10000000
χ424444-14-144400-4-1-1-1-1-14-14440011-4-4-1-1-1-1-1-100111100-40-1-10000000000000000110000000
χ434444-14-14-4-4004-1-1-1-1-14-14-4-400-1-144-1-1-1-11100-1-1-1-100-40110000000000000000110000000
χ444444-14-14-4-400-4-1-1-1-1-14-14-4-40011-4-4-1-1-1-1110011110040110000000000000000-1-10000000
χ454-44-44-1-41004i−4i0-1-1114-1-41004i−4i00−55-1-11100−ii−5−555000000−ii0000000000000000−i5i500000
χ464-44-44-1-41004i−4i0-1-1114-1-41004i−4i005−5-1-11100−ii55−5−5000000−ii0000000000000000i5−i500000
χ474-44-44-1-4100−4i4i0-1-1114-1-4100−4i4i00−55-1-11100i−i−5−555000000i−i0000000000000000i5−i500000
χ484-44-44-1-4100−4i4i0-1-1114-1-4100−4i4i005−5-1-11100i−i55−5−5000000i−i0000000000000000−i5i500000
χ494-44-4-141-44i−4i000-1-111-141-44i−4i00−5500-1-111−ii00−55−550000−ii0000000000000000−i5i50000000
χ504-44-4-141-44i−4i000-1-111-141-44i−4i005−500-1-111−ii005−55−50000−ii0000000000000000i5−i50000000
χ514-44-4-141-4−4i4i000-1-111-141-4−4i4i00−5500-1-111i−i00−55−550000i−i0000000000000000i5−i50000000
χ524-44-4-141-4−4i4i000-1-111-141-4−4i4i005−500-1-111i−i005−55−50000i−i0000000000000000−i5i50000000
χ538888-2-2-2-2000083-23-2-2-2-2-20000-2-2-2-23-23-200003-2-230000000000000000000000000000000
χ548888-2-2-2-200008-23-23-2-2-2-20000-2-2-2-2-23-230000-233-20000000000000000000000000000000
χ558888-2-2-2-20000-83-23-2-2-2-2-2000022223-23-20000-322-30000000000000000000000000000000
χ568888-2-2-2-20000-8-23-23-2-2-2-200002222-23-2300002-3-320000000000000000000000000000000
χ5788-4-48-28-200880-2-2-2-2-41-4100-4-40000111100-2-200000000001100000000000000000000000
χ5888-4-48-28-200-8-80-2-2-2-2-41-4100440000111100220000000000-1-100000000000000000000000
χ5988-4-4-28-2888000-2-2-2-21-41-4-4-40000001111-2-20000000000110000000000000000000000000
χ6088-4-4-28-28-8-8000-2-2-2-21-41-4440000001111220000000000-1-10000000000000000000000000
χ618-88-8-2-222000003-2-32-2-2220000−2525−25253-2-320000500−50000000000000000000000000000000
χ628-88-8-2-222000003-2-32-2-222000025−2525−253-2-320000−50050000000000000000000000000000000
χ638-88-8-2-22200000-232-3-2-2220000−252525−25-232-300000−5500000000000000000000000000000000
χ648-88-8-2-22200000-232-3-2-222000025−25−2525-232-3000005−500000000000000000000000000000000
χ658-8-448-2-82008i−8i0-2-222-414-100−4i4i000011-1-100−2i2i0000000000i−i00000000000000000000000
χ668-8-448-2-8200−8i8i0-2-222-414-1004i−4i000011-1-1002i−2i0000000000−ii00000000000000000000000
χ678-8-44-282-88i−8i000-2-2221-4-14−4i4i00000011-1-1−2i2i0000000000i−i0000000000000000000000000
χ688-8-44-282-8−8i8i000-2-2221-4-144i−4i00000011-1-12i−2i0000000000−ii0000000000000000000000000
χ691616-8-8-4-4-4-4000006-46-4222200000000-32-32000000000000000000000000000000000000000
χ701616-8-8-4-4-4-400000-46-462222000000002-32-3000000000000000000000000000000000000000
χ7116-16-88-4-444000006-4-6422-2-200000000-323-2000000000000000000000000000000000000000
χ7216-16-88-4-44400000-464-622-2-2000000002-3-23000000000000000000000000000000000000000

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