Finite Group Databasebeta

← Group #72259927

Character table — Group #72259927

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222444444666888888889916161616181818181818181818182424242424243636363636363636363636363636545454545454545454727272727272108108216216
order123366333666412123333666622336644666612121212121212121212226666661212121212124441212121212126666662266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1-1-11111111-111-1-111-1-1-1-1-1-11-1-111-1-1-1-11-111-1-11-11-1
χ411111111111111111111111111111-1-11111-1-1-1-1111111-11-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-11-1-111-11-11
χ5111111111111-1-1-1111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-111-1-111111-111-1-1-11-11
χ8111111111111-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-111-1-11111-11-1-1111-11-1
χ922222222222222222222222-2-2222200-2-2-2-20000222222000000-2-2000000-200-2-200000000000000
χ10222222222222-2-2-222222222-2-2222200-2-2-2-20000-2-2-2-2-2-2000000-2-20000002002200000000000000
χ11222-1-12-122-12200022-1-1-1-12222-1-1-1-122-12-12222200000022-1-1-1-1-1-1-1-1-1-1-1-100000000022-1-1-1-10000
χ12222-1-12-122-12200022-1-1-1-12222-1-1-1-122-12-122222000000-2-21111-1-1-1-1-1-1-1-1000000000-2-211110000
χ13222-1-12-122-12200022-1-1-1-12222-1-1-1-1-2-2-12-12-2-2-2-20000002-2-1-111-1-11111110000000002-2-1-1110000
χ14222-1-12-122-12200022-1-1-1-12222-1-1-1-1-2-2-12-12-2-2-2-2000000-2211-1-1-1-1111111000000000-2211-1-10000
χ1522-122-1-122-1222-1-1-1-12222-1-122-1-1-1-1222-12-1-1-1-1-122-1-1-1-1000000-1-122-1-1-1-1222-1-1-1-1-1-10000000000
χ1622-122-1-122-1222-1-1-1-12222-1-122-1-1-1-1-2-22-12-1111122-1-1-1-1000000-1-1-2-211112-2-2-1-111110000000000
χ1722-122-1-122-1222-1-1-1-12222-1-1-2-2-1-1-1-100-21-2133−3−322-1-1-1-1000000110033−3−3-2001133−3−30000000000
χ1822-122-1-122-1222-1-1-1-12222-1-1-2-2-1-1-1-100-21-21−3−33322-1-1-1-10000001100−3−333-20011−3−3330000000000
χ1922-122-1-122-122-211-1-12222-1-122-1-1-1-1222-12-1-1-1-1-1-2-21111000000-1-122-1-1-1-1-2-2-21111110000000000
χ2022-122-1-122-122-211-1-12222-1-122-1-1-1-1-2-22-12-11111-2-21111000000-1-1-2-21111-22211-1-1-1-10000000000
χ2122-122-1-122-122-211-1-12222-1-1-2-2-1-1-1-100-21-2133−3−3-2-21111000000110033−3−3200-1-1−3−3330000000000
χ2222-122-1-122-122-211-1-12222-1-1-2-2-1-1-1-100-21-21−3−333-2-211110000001100−3−333200-1-133−3−30000000000
χ232-222-2-2222-2-2-20002222-2-2-2-22-222-2-22-2-222-22-22-2000000000000-222-22-22-20000000000000000000
χ242-222-2-2222-2-2-20002222-2-2-2-22-222-2-2-22-222-2-22-22000000000000-22-22-22-220000000000000000000
χ252-222-2-2222-2-2-20002222-2-2-2-2-2222-2-2002-2-2200000000000000002-200000002-2002-22-20000000000
χ262-222-2-2222-2-2-20002222-2-2-2-2-2222-2-2002-2-2200000000000000002-20000000-2200-22-220000000000
χ272-22-11-2-1221-2-200022-1-111-2-22-2-1-1112-212-1-22-22-200000000−i3i3−i3i31-1-11-11-1100000000000−i3i3−i3i30000
χ282-22-11-2-1221-2-200022-1-111-2-22-2-1-1112-212-1-22-22-200000000i3−i3i3−i31-1-11-11-1100000000000i3−i3i3−i30000
χ292-22-11-2-1221-2-200022-1-111-2-22-2-1-111-2212-1-2-22-2200000000−i3i3i3−i31-11-11-11-100000000000−i3i3i3−i30000
χ302-22-11-2-1221-2-200022-1-111-2-22-2-1-111-2212-1-2-22-2200000000i3−i3−i3i31-11-11-11-100000000000i3−i3−i3i30000
χ312-2-12-21-1221-2-203−3-1-122-2-2112-2-1-1112-2-2-121-11-110033−3−30000001-12-2-11-110003−33−3−330000000000
χ322-2-12-21-1221-2-203−3-1-122-2-2112-2-1-111-22-2-1211-11-10033−3−30000001-1-221-11-10003−3−333−30000000000
χ332-2-12-21-1221-2-203−3-1-122-2-211-22-1-1110021-2-13−3−330033−3−3000000-11003−3−330-22−331-11-10000000000
χ342-2-12-21-1221-2-203−3-1-122-2-211-22-1-1110021-2-1−333−30033−3−3000000-1100−333−302-2−33-11-110000000000
χ352-2-12-21-1221-2-20−33-1-122-2-2112-2-1-1112-2-2-121-11-1100−3−3330000001-12-2-11-11000−33−333−30000000000
χ362-2-12-21-1221-2-20−33-1-122-2-2112-2-1-111-22-2-1211-11-100−3−3330000001-1-221-11-1000−333−3−330000000000
χ372-2-12-21-1221-2-20−33-1-122-2-211-22-1-1110021-2-13−3−3300−3−333000000-11003−3−3302-23−3-11-110000000000
χ382-2-12-21-1221-2-20−33-1-122-2-211-22-1-1110021-2-1−333−300−3−333000000-1100−333−30-223−31-11-10000000000
χ3944444441-241-24441-21-21-21-2001-21-200000000001-21-21-2020022000000000000000000-100-1-1020-1
χ4044444441-241-24441-21-21-21-2001-21-200000000001-21-21-20-200-2-2000000000000000000100110-201
χ4144444441-241-2-4-4-41-21-21-21-2001-21-20000000000-12-12-12020022000000000000000000-100-1-10-201
χ4244444441-241-2-4-4-41-21-21-21-2001-21-20000000000-12-12-120-200-2-200000000000000000010011020-1
χ434444444-214-21444-21-21-21-2100-21-210000000000-21-21-2120220000000000000000000-10-1-10020-10
χ444444444-214-21444-21-21-21-2100-21-210000000000-21-21-21-20-2-20000000000000000000101100-2010
χ454444444-214-21-4-4-4-21-21-21-2100-21-2100000000002-12-12-120220000000000000000000-10-1-100-2010
χ464444444-214-21-4-4-4-21-21-21-2100-21-2100000000002-12-12-1-20-2-2000000000000000000010110020-10
χ47444-2-24-244-24400044-2-2-2-244-4-4-2-2-2-2002-42-40000000000000000220000000000000000000000000
χ4844-2-2-2-2144144000-2-2-2-2-2-2-2-244111144-2-2-2-2-2-2-2-200000000000011-2-211110000000000000000000
χ4944-2-2-2-2144144000-2-2-2-2-2-2-2-2441111-4-4-2-2-2-222220000000000001122-1-1-1-10000000000000000000
χ5044-2-2-2-2144144000-2-2-2-2-2-2-2-2-4-411110022222323−23−23000000000000-1-100−3−3330000000000000000000
χ5144-2-2-2-2144144000-2-2-2-2-2-2-2-2-4-41111002222−23−232323000000000000-1-10033−3−30000000000000000000
χ524-44-22-4-2442-4-400044-2-222-4-4-44-2-22200-2-4240000000000000000-220000000000000000000000000
χ534-4-2-222144-1-4-4000-2-2-2-222224-411-1-14-42-2-22-22-22000000000000-11-221-11-10000000000000000000
χ544-4-2-222144-1-4-4000-2-2-2-222224-411-1-1-442-2-222-22-2000000000000-112-2-11-110000000000000000000
χ554-4-2-222144-1-4-4000-2-2-2-22222-4411-1-100-222-223−23−23230000000000001-100−333−30000000000000000000
χ564-4-2-222144-1-4-4000-2-2-2-22222-4411-1-100-222-2−232323−230000000000001-1003−3−330000000000000000000
χ57888-4-48-42-4-42-40002-4-12-122-400-12-1200000000000000000400-2-2000000000000000000-200110000
χ58888-4-48-42-4-42-40002-4-12-122-400-12-1200000000000000000-40022000000000000000000200-1-10000
χ59888-4-48-4-42-4-42000-422-12-1-42002-12-1000000000000000040-2-20000000000000000000-2011000000
χ60888-4-48-4-42-4-42000-422-12-1-42002-12-10000000000000000-4022000000000000000000020-1-1000000
χ6188-488-4-42-4-42-48-4-4-122-42-4-1200-12-1200000000002-4-12-12000000000000000000000000000000000
χ6288-488-4-42-4-42-4-844-122-42-4-1200-12-120000000000-241-21-2000000000000000000000000000000000
χ6388-488-4-4-42-4-428-4-42-1-42-422-1002-12-10000000000-422-12-1000000000000000000000000000000000
χ6488-488-4-4-42-4-42-8442-1-42-422-1002-12-100000000004-2-21-21000000000000000000000000000000000
χ658-888-8-882-4-8-240002-42-4-24-24002-4-240000000000000000000000000000000000000000000000000
χ668-888-8-88-42-84-2000-42-424-24-200-424-20000000000000000000000000000000000000000000000000
χ678-88-44-8-42-44-240002-4-121-2-2400-121-200000000000000000000−2i32i3000000000000000000000i3−i30000
χ688-88-44-8-42-44-240002-4-121-2-2400-121-2000000000000000000002i3−2i3000000000000000000000−i3i30000
χ698-88-44-8-4-4244-2000-422-1-214-2002-1-21000000000000000000−2i32i3000000000000000000000i3−i3000000
χ708-88-44-8-4-4244-2000-422-1-214-2002-1-210000000000000000002i3−2i3000000000000000000000−i3i3000000
χ718-8-48-84-42-44-24043−43-122-4-241-200-121-20000000000003−23−323000000000000000000000000000000000
χ728-8-48-84-42-44-240−4343-122-4-241-200-121-2000000000000−3233−23000000000000000000000000000000000
χ738-8-48-84-4-4244-2043−432-1-424-2-21002-1-21000000000000−23323−3000000000000000000000000000000000
χ748-8-48-84-4-4244-20−43432-1-424-2-21002-1-2100000000000023−3−233000000000000000000000000000000000
χ751616-8-8-8-844-844-8000-24-24-24-24001-21-20000000000000000000000000000000000000000000000000
χ761616-8-8-8-84-844-840004-24-24-24-200-21-210000000000000000000000000000000000000000000000000
χ7716-16-8-88844-8-4-48000-24-242-42-4001-2-120000000000000000000000000000000000000000000000000
χ7816-16-8-8884-84-48-40004-24-2-42-4200-212-10000000000000000000000000000000000000000000000000

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