Finite Group Databasebeta

← Group #13139171

Character table — Group #13139171

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222224466668881212121212121212121218182424242424242424242436363636363636363672727272727272727272727272
order1223446121261233668242436661212121212128861224242424242424242488824242424226666681224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-11-111-1-1
χ31111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-11-1-1-1111-11-1-1-1-1
χ41111111111111111111111111111-1-11111111111-1-1-111-1-1-1-1-1111-1-1-1-1-1-1-111
χ5111111111111111-1-1-111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-11-1-111
χ6111111111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111-111-1-1-1-1-1-1
χ7111111111111111-1-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ8111111111111111-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-11111
χ9222222222222-12-1222-12-1-1-12-1-1-1200-1-122-1-1-1-1-1-12200000002000-1-1-10-10000
χ10222222222222-12-1222-12-1-1-12-1-1-1200-1-122-1-1-1-1-1-1-2-20000000-2000111010000
χ11222222222222-12-1-2-2-2-12-1-1-12-1-1-1200-1-1-2-2111111220000000-2000-1110-10000
χ12222222222222-12-1-2-2-2-12-1-1-12-1-1-1200-1-1-2-2111111-2-2000000020001-1-1010000
χ1322222222222-12-12222-1-12-12-12-1-1-100-1-1-1-122-1-1-1-100022000002-1-10000000-1-1
χ1422222222222-12-12222-1-12-12-12-1-1-100-1-1-1-122-1-1-1-1000-2-200000-211000000011
χ1522222222222-12-12-2-2-2-1-12-12-12-1-1-100-1-111-2-211110002200000-2110000000-1-1
χ1622222222222-12-12-2-2-2-1-12-12-12-1-1-100-1-111-2-21111000-2-2000002-1-1000000011
χ172222-2-22-2-22-222220002222-2-2-2-2-2-2002-2000000000002i−2i0000000000000002i−2i
χ182222-2-22-2-22-222220002222-2-2-2-2-2-2002-200000000000−2i2i000000000000000−2i2i
χ192222-2-22-2-22-2-12-12000-1-12-1-21-211100-113−30033−3−30002i−2i000000−i3i30000000−ii
χ202222-2-22-2-22-2-12-12000-1-12-1-21-211100-113−30033−3−3000−2i2i000000i3−i30000000i−i
χ212222-2-22-2-22-2-12-12000-1-12-1-21-211100-11−3300−3−3330002i−2i000000i3−i30000000−ii
χ222222-2-22-2-22-2-12-12000-1-12-1-21-211100-11−3300−3−333000−2i2i000000−i3i30000000i−i
χ2322-222-2222-2-222220002-2-22-22222-200-2-2000000002-2000000000002000-20000
χ2422-222-2222-2-222220002-2-22-22222-200-2-200000000-2200000000000-200020000
χ2522-222-2222-2-22-12-1000-1-21-112-1-1-1-2001100−i3i3−i3i3−i3i32-200000000000-1−i3i3010000
χ2622-222-2222-2-22-12-1000-1-21-112-1-1-1-2001100−i3i3−i3i3−i3i3-22000000000001i3−i30-10000
χ2722-222-2222-2-22-12-1000-1-21-112-1-1-1-2001100i3−i3i3−i3i3−i32-200000000000-1i3−i3010000
χ2822-222-2222-2-22-12-1000-1-21-112-1-1-1-2001100i3−i3i3−i3i3−i3-22000000000001−i3i30-10000
χ2922-22-222-2-2-2222220002-2-222-2-2-2-2222-220000000000-20022-2-20000000000000
χ3022-22-222-2-2-2222220002-2-222-2-2-2-22-2-2-220000000000200-2-2220000000000000
χ3144444444444-2-2-2-24441-2-21-2-2-211-20011-2-2-2-211110000000000000000000000
χ3244444444444-2-2-2-2-4-4-41-2-21-2-2-211-200112222-1-1-1-10000000000000000000000
χ334444-4-44-4-44-44-24-2000-24-2-22-4222-400-22000000000000000000000000000000
χ344444-4-44-4-44-4-2-2-2-20001-2-21222-1-12001-123−2300−3−3330000000000000000000000
χ354444-4-44-4-44-4-2-2-2-20001-2-21222-1-12001-1−23230033−3−30000000000000000000000
χ3644-444-4444-4-4-24-24000-22-4-2-4-24-2-220022000000000000000000000000000000
χ3744-444-4444-4-4-2-2-2-200012212-2-211200-1-100−2i32i3i3−i3i3−i30000000000000000000000
χ3844-444-4444-4-4-2-2-2-200012212-2-211200-1-1002i3−2i3−i3i3−i3i30000000000000000000000
χ3944-44-444-4-4-444-24-2000-2-42-2-2-42224002-2000000000000000000000000000000
χ4044-44-444-4-4-44-24-24000-22-4-242-422-2002-2000000000000000000000000000000
χ4144-44-444-4-4-44-2-2-2-20001221-222-1-1-200-1100003i−3i−3i3i0000000000000000000000
χ4244-44-444-4-4-44-2-2-2-20001221-222-1-1-200-110000−3i3i3i−3i0000000000000000000000
χ434-40400-4000044-4-4000400-400000022−2200000000000000022−22000000000000000
χ444-40400-4000044-4-4000400-4000000−2222000000000000000−2222000000000000000
χ45666-366-3-3-3-3-300006-3-3000000000022000000000000200-1-1-1-1000000020-1-100
χ46666-366-3-3-3-3-300006-3-30000000000-2-2000000000000-20011110000000-201100
χ47666-366-3-3-3-3-30000-633000000000022000000000000200-1-1-1-10000000-201100
χ48666-366-3-3-3-3-30000-6330000000000-2-2000000000000-2001111000000020-1-100
χ4966-6-3-66-3333-30000033−33000000000022000000000000-200-1-1110000000003−300
χ5066-6-3-66-3333-30000033−330000000000-2-200000000000020011-1-1000000000−3300
χ5166-6-3-66-3333-300000−3333000000000022000000000000-200-1-111000000000−3300
χ5266-6-3-66-3333-300000−33330000000000-2-200000000000020011-1-10000000003−300
χ538-80800-800008-4-84000-40040000000000000000000000000000000000000000
χ548-80800-80000-484-8000-40040000000000000000000000000000000000000000
χ558-80800-80000-4-444000200-20006i−6i00000000000000000000000000000000000
χ568-80800-80000-4-444000200-2000−6i6i00000000000000000000000000000000000
χ57121212-6-12-12-666-66000000000000000000000000000000000000000000000000000
χ581212-12-612-12-6-6-666000000000000000000000000000000000000000000000000000
χ5912-120-600663−63000000000000000000022−22000000000000000−226−60000000000000
χ6012-120-600663−630000000000000000000−22220000000000000002−2−660000000000000
χ6112-120-6006−6363000000000000000000022−22000000000000000−22−660000000000000
χ6212-120-6006−63630000000000000000000−22220000000000000002−26−60000000000000

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