Finite Group Databasebeta

← Group #72222970

Character table — Group #72222970

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222334466666666991212121212121212121212121818242424242424272748484848484854545454545454545454727272727272108108108108108108108108
order1233662236366666664436666666666612123336664433366622444444121212121212121266121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1111111111111-1-1111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1111111111111-1-1111111-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51-111-1-11-11-111-1-111-1-1i−i11-11-1111-1-1-1-1i−i111-1-1-1i−i111-1-1-11-1i−i1-1i−ii−iiii−i−i−i1-11-1ii−i−i
χ61-111-1-11-11-111-1-111-1-1i−i11-11-1111-1-1-1-1i−i111-1-1-1i−i111-1-1-1-11−ii-11−iii−iiii−i−i−i-11-11−i−iii
χ71-111-1-11-11-111-1-111-1-1−ii11-11-1111-1-1-1-1−ii111-1-1-1−ii111-1-1-11-1−ii1-1−ii−ii−i−i−iiii1-11-1−i−iii
χ81-111-1-11-11-111-1-111-1-1−ii11-11-1111-1-1-1-1−ii111-1-1-1−ii111-1-1-1-11i−i-11i−i−ii−i−i−iiii-11-11ii−i−i
χ92222222222222222222222222222222222-1-1-1-1-1-122-1-1-1-1-1-10000000022-1-1-1-1-1-100000000
χ10222222222222222222-2-2222222222222-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-100000000-2-211111100000000
χ112222222222-1222-12-1-100-122-1-1-1-1-1-1-1-1-10022222200-1-1-1-1-1-100220022000000000000-1-1-1-1
χ122222222222-1222-12-1-100-122-1-1-1-1-1-1-1-1-10022222200-1-1-1-1-1-100-2-200-2-20000000000001111
χ1322-122-122-1-12-1-12222222-1-1-122-1-1-1-1-1-1-1-1-12-1-12-1-1222-1-12-1-100000000-1-12-1-12-1-100000000
χ1422-122-122-1-12-1-12222222-1-1-122-1-1-1-1-1-1-1-1-1-12-1-12-122-12-1-12-100000000-1-1-12-1-12-100000000
χ1522-122-122-1-12-1-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1-12-1-1222-1-12-1-1200000000-1-1-1-12-1-1200000000
χ1622-122-122-1-12-1-122222-2-2-1-1-122-1-1-1-1-1-1-1112-1-12-1-1-2-22-1-12-1-10000000011-211-21100000000
χ1722-122-122-1-12-1-122222-2-2-1-1-122-1-1-1-1-1-1-111-12-1-12-1-2-2-12-1-12-100000000111-211-2100000000
χ1822-122-122-1-12-1-122222-2-2-1-1-122-1-1-1-1-1-1-111-1-12-1-12-2-2-1-12-1-12000000001111-211-200000000
χ192-222-2-22-22-222-2-222-2-22i−2i22-22-2222-2-2-2-22i−2i-1-1-11112i−2i-1-1-1111000000002i−2i−i−i−iiii00000000
χ202-222-2-22-22-222-2-222-2-2−2i2i22-22-2222-2-2-2-2−2i2i-1-1-1111−2i2i-1-1-111100000000−2i2iiii−i−i−i00000000
χ212-222-2-22-22-2-12-2-2-121100-12-2-11-1-1-1111100222-2-2-200-1-1-1111002i−2i002i−2i000000000000−i−iii
χ222-222-2-22-22-2-12-2-2-121100-12-2-11-1-1-1111100222-2-2-200-1-1-111100−2i2i00−2i2i000000000000ii−i−i
χ232-2-12-212-2-112-11-222-2-22i−2i-1-112-2-1-1-11111−ii2-1-1-2112i−2i2-1-1-21100000000−ii2i−i−i−2iii00000000
χ242-2-12-212-2-112-11-222-2-22i−2i-1-112-2-1-1-11111−ii-12-11-212i−2i-12-11-2100000000−ii−i2i−ii−2ii00000000
χ252-2-12-212-2-112-11-222-2-22i−2i-1-112-2-1-1-11111−ii-1-1211-22i−2i-1-1211-200000000−ii−i−i2iii−2i00000000
χ262-2-12-212-2-112-11-222-2-2−2i2i-1-112-2-1-1-11111i−i2-1-1-211−2i2i2-1-1-21100000000i−i−2iii2i−i−i00000000
χ272-2-12-212-2-112-11-222-2-2−2i2i-1-112-2-1-1-11111i−i-12-11-21−2i2i-12-11-2100000000i−ii−2ii−i2i−i00000000
χ282-2-12-212-2-112-11-222-2-2−2i2i-1-112-2-1-1-11111i−i-1-1211-2−2i2i-1-1211-200000000i−iii−2i−i−i2i00000000
χ29333333-1-1333-1-1-1-1-13-1333-1-1-1-1-1-1-13-1-1-133000000-1-10000001111-1-1-1-1-1-100000011-1-11-11-1
χ30333333-1-1333-1-1-1-1-13-1333-1-1-1-1-1-1-13-1-1-133000000-1-1000000-1-1-1-11111-1-1000000-1-111-11-11
χ31333333-1-1333-1-1-1-1-13-1-3-33-1-1-1-1-1-1-13-1-1-1-3-30000001100000011-1-1-1-1111100000011-1-1-11-11
χ32333333-1-1333-1-1-1-1-13-1-3-33-1-1-1-1-1-1-13-1-1-1-3-300000011000000-1-11111-1-111000000-1-1111-11-1
χ333-333-3-3-113-33-111-1-1-313i−3i3-11-11-1-1-1-31113i−3i000000−ii0000001-1i−i-11−ii−ii0000001-1-11i−i−ii
χ343-333-3-3-113-33-111-1-1-313i−3i3-11-11-1-1-1-31113i−3i000000−ii000000-11−ii1-1i−i−ii000000-111-1−iii−i
χ353-333-3-3-113-33-111-1-1-31−3i3i3-11-11-1-1-1-3111−3i3i000000i−i0000001-1−ii-11i−ii−i0000001-1-11−iii−i
χ363-333-3-3-113-33-111-1-1-31−3i3i3-11-11-1-1-1-3111−3i3i000000i−i000000-11i−i1-1−iii−i000000-111-1i−i−ii
χ374444444444-2444-24-2-200-244-2-2-2-2-2-2-2-2-200-2-2-2-2-2-200111111000000000000000000000000
χ3844-244-244-2-2-2-2-24-24-2-2001-2-2-2-21111111004-2-24-2-200-211-211000000000000000000000000
χ3944-244-244-2-2-2-2-24-24-2-2001-2-2-2-2111111100-24-2-24-2001-211-21000000000000000000000000
χ4044-244-244-2-2-2-2-24-24-2-2001-2-2-2-2111111100-2-24-2-240011-211-2000000000000000000000000
χ414-444-4-44-44-4-24-4-4-242200-24-4-22-2-2-2222200-2-2-222200111-1-1-1000000000000000000000000
χ424-4-24-424-4-22-2-22-4-2422001-22-22111-1-1-1-1004-2-2-42200-2112-1-1000000000000000000000000
χ434-4-24-424-4-22-2-22-4-2422001-22-22111-1-1-1-100-24-22-42001-21-12-1000000000000000000000000
χ444-4-24-424-4-22-2-22-4-2422001-22-22111-1-1-1-100-2-2422-40011-2-1-12000000000000000000000000
χ45666666-2-266-3-2-2-21-2-3100-3-2-211111-31110000000000000000002200-2-2000000000000-11-11
χ46666666-2-266-3-2-2-21-2-3100-3-2-211111-3111000000000000000000-2-200220000000000001-11-1
χ47666-3-3666-3-3066-30-300000-3-300000000000000000000000002200220000000000-1-1-1-10000
χ48666-3-3666-3-3066-30-300000-3-30000000000000000000000000-2-200-2-2000000000011110000
χ49666-3-36-2-2-3-30-2-21410400011-2-24-2-204-2-200000000000000002200-2-20000000000-1-1110000
χ50666-3-36-2-2-3-30-2-21410400011-2-24-2-204-2-20000000000000000-2-20022000000000011-1-10000
χ5166-366-3-2-2-3-3611-2-2-26-266-311-2-2111-3111-3-3000000-2-2000000000000001100000000000000
χ5266-366-3-2-2-3-3611-2-2-26-2-6-6-311-2-2111-3111330000002200000000000000-1-100000000000000
χ536-666-6-6-226-6-3-2221-23-100-3-221-11113-1-1-10000000000000000002i−2i00−2i2i000000000000−iii−i
χ546-666-6-6-226-6-3-2221-23-100-3-221-11113-1-1-1000000000000000000−2i2i002i−2i000000000000i−i−ii
χ556-66-33-66-6-3306-630-300000-3300000000000000000000000002-2002-20000000000-11-110000
χ566-66-33-66-6-3306-630-300000-330000000000000000000000000-2200-2200000000001-11-10000
χ576-66-33-6-22-330-22-1410-40001-1-224-2-20-42200000000000000002-200-220000000000-111-10000
χ586-66-33-6-22-330-22-1410-40001-1-224-2-20-4220000000000000000-22002-200000000001-1-110000
χ596-6-36-63-22-3361-12-2-2-626i−6i-31-1-221113-1-1-1−3i3i000000−2i2i00000000000000i−i00000000000000
χ606-6-36-63-22-3361-12-2-2-62−6i6i-31-1-221113-1-1-13i−3i0000002i−2i00000000000000−ii00000000000000
χ61121212-6-612-4-4-6-60-4-42-420-40002222-4220-4220000000000000000000000000000000000000000
χ621212-61212-6-4-4-6-6-622-42-4-620032222-1-1-13-1-1-10000000000000000000000000000000000000000
χ631212-6-6-6-61212330-6-6-60-600000330000000000000000000000000000000000000000000000000
χ641212-6-6-6-6-4-43302228208000-1-1-4-4-4220-4220000000000000000000000000000000000000000
χ651212-6-6-6-6-4-4330222-420-4000-1-1222−1−3i3−1+3i302−1−3i3−1+3i30000000000000000000000000000000000000000
χ661212-6-6-6-6-4-4330222-420-4000-1-1222−1+3i3−1−3i302−1+3i3−1−3i30000000000000000000000000000000000000000
χ6712-1212-66-12-44-660-44-2-42040002-22-2-42204-2-20000000000000000000000000000000000000000
χ6812-12-612-126-44-66-62-242-46-20032-22-2-1-1-1-31110000000000000000000000000000000000000000
χ6912-12-6-66612-123-30-6660-6000003-30000000000000000000000000000000000000000000000000
χ7012-12-6-666-443-302-2-2820-8000-11-44-42204-2-20000000000000000000000000000000000000000
χ7112-12-6-666-443-302-2-2-4204000-112-22−1−3i3−1+3i30-21+3i31−3i30000000000000000000000000000000000000000
χ7212-12-6-666-443-302-2-2-4204000-112-22−1+3i3−1−3i30-21−3i31+3i30000000000000000000000000000000000000000

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