Finite Group Databasebeta

← Group #13167584

Character table — Group #13167584

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444448888888888888888888899991818181836363636363636363636363636363636363636363636367272727272727272
order12223666233666666663366666666666666666622226666222444444444466121212121212121266121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ511111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111
χ711111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1
χ811111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ9222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2000000000000-2-20000000000000000
χ1022222222-222-2-222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22000000000000220000000000000000
χ112222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12000000002222-1-1-1-1-1-1-1-1-1-100000000
χ122222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1200000000-2-2-2-2-1-11111111100000000
χ132222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-20000000000001133−3−333−3−300000000
χ142222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-200000000000011−3−333−3−33300000000
χ152222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-1111111112222-1-1-1-1-20000000022-2-211-1-1-1-1111100000000
χ162222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-1111111112222-1-1-1-1-200000000-2-222111111-1-1-1-100000000
χ172222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-211112000000000000-1-133−3−3−3−33300000000
χ182222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-211112000000000000-1-1−3−33333−3−300000000
χ1922-2-222-2-20220022-2-2-2-222000022-2-2-2-2000000002-22-22-22-200000002i−2i000000000000000000002i−2i
χ2022-2-222-2-20220022-2-2-2-222000022-2-2-2-2000000002-22-22-22-20000000−2i2i00000000000000000000−2i2i
χ2122-2-222-2-20220022-2-2-2-222000022-2-2-2-200000000-22-22-22-220002i−2i00000000000000000000002i−2i00
χ2222-2-222-2-20220022-2-2-2-222000022-2-2-2-200000000-22-22-22-22000−2i2i0000000000000000000000−2i2i00
χ232-22-22-22-202200-2-222-2-2220000-2-222-2-20000000022-2-222-2-2000000000002i−2i0000002i−2i2i−2i00000000
χ242-22-22-22-202200-2-222-2-2220000-2-222-2-20000000022-2-222-2-200000000000−2i2i000000−2i2i−2i2i00000000
χ252-22-22-22-202200-2-222-2-2220000-2-222-2-200000000-2-222-2-2220000000002-200002-22-2000000000000
χ262-22-22-22-202200-2-222-2-2220000-2-222-2-200000000-2-222-2-222000000000-220000-22-22000000000000
χ272-22-2-11-11022−i3i3-2-222-2-2-1-1000011-1-111−i3−i3−i3−i3i3i3i3i322-2-2-1-111000000000002i−2i−i3i33−3−33−ii−ii00000000
χ282-22-2-11-11022−i3i3-2-222-2-2-1-1000011-1-111−i3−i3−i3−i3i3i3i3i322-2-2-1-11100000000000−2i2i−i3i3−333−3i−ii−i00000000
χ292-22-2-11-11022−i3i3-2-222-2-2-1-1000011-1-111−i3−i3−i3−i3i3i3i3i3-2-22211-1-10000000002-200i3−i3-11-11−i3i3i3−i300000000
χ302-22-2-11-11022−i3i3-2-222-2-2-1-1000011-1-111−i3−i3−i3−i3i3i3i3i3-2-22211-1-1000000000-2200i3−i31-11-1i3−i3−i3i300000000
χ312-22-2-11-11022i3−i3-2-222-2-2-1-1000011-1-111i3i3i3i3−i3−i3−i3−i322-2-2-1-111000000000002i−2ii3−i3−333−3−ii−ii00000000
χ322-22-2-11-11022i3−i3-2-222-2-2-1-1000011-1-111i3i3i3i3−i3−i3−i3−i322-2-2-1-11100000000000−2i2ii3−i33−3−33i−ii−i00000000
χ332-22-2-11-11022i3−i3-2-222-2-2-1-1000011-1-111i3i3i3i3−i3−i3−i3−i3-2-22211-1-10000000002-200−i3i3-11-11i3−i3−i3i300000000
χ342-22-2-11-11022i3−i3-2-222-2-2-1-1000011-1-111i3i3i3i3−i3−i3−i3−i3-2-22211-1-1000000000-2200−i3i31-11-1−i3i3i3−i300000000
χ352-2-222-2-2202200-2-2-2-222220000-2-2-2-222000000002-2-222-2-2202-2000000000000000000002-2000000
χ362-2-222-2-2202200-2-2-2-222220000-2-2-2-222000000002-2-222-2-220-2200000000000000000000-22000000
χ372-2-222-2-2202200-2-2-2-222220000-2-2-2-22200000000-222-2-222-2000002-20000000000000000002-20000
χ382-2-222-2-2202200-2-2-2-222220000-2-2-2-22200000000-222-2-222-200000-22000000000000000000-220000
χ394444444441-2441-2-211-21-211-2-21-21-21-211-2-211-2-200000000000220022000000000000000000-1-1-1-1
χ404444444441-2441-2-211-21-211-2-21-21-21-211-2-211-2-200000000000-2-200-2-20000000000000000001111
χ41444444444-2144-211-2-21-21-2-211-21-21-21-2-211-2-2110000000002200220000000000000000-1-1-1-10000
χ42444444444-2144-211-2-21-21-2-211-21-21-21-2-211-2-211000000000-2-200-2-2000000000000000011110000
χ4344444444-41-2-4-41-2-211-21-2-1-1221-21-21-2-1-122-1-122000000000002200-2-2000000000000000000-1-111
χ4444444444-41-2-4-41-2-211-21-2-1-1221-21-21-2-1-122-1-12200000000000-2-2002200000000000000000011-1-1
χ4544444444-4-21-4-4-211-2-21-2122-1-1-21-21-2122-1-122-1-10000000002200-2-20000000000000000-1-1110000
χ4644444444-4-21-4-4-211-2-21-2122-1-1-21-21-2122-1-122-1-1000000000-2-20022000000000000000011-1-10000
χ4744-4-444-4-401-2001-22-1-121-23-3001-2-12-123-3003-300000000000002i−2i002i−2i000000000000000000−ii−ii
χ4844-4-444-4-401-2001-22-1-121-23-3001-2-12-123-3003-30000000000000−2i2i00−2i2i000000000000000000i−ii−i
χ4944-4-444-4-401-2001-22-1-121-2-33001-2-12-12-3300-3300000000000002i−2i00−2i2i000000000000000000−iii−i
χ5044-4-444-4-401-2001-22-1-121-2-33001-2-12-12-3300-330000000000000−2i2i002i−2i000000000000000000i−i−ii
χ5144-4-4-2-2220440044-4-4-4-4-2-20000-2-22222000000004-44-4-22-220000000000000000000000000000000
χ5244-4-4-2-2220440044-4-4-4-4-2-20000-2-2222200000000-44-442-22-20000000000000000000000000000000
χ534-4-444-4-440-21002-1-12-21-21003-32-12-1-21003-3003-30000000002-2002-20000000000000000-11-110000
χ544-4-444-4-440-21002-1-12-21-21003-32-12-1-21003-3003-3000000000-2200-2200000000000000001-11-10000
χ554-4-444-4-440-21002-1-12-21-2100-332-12-1-2100-3300-330000000002-200-220000000000000000-111-10000
χ564-4-444-4-440-21002-1-12-21-2100-332-12-1-2100-3300-33000000000-22002-200000000000000001-1-110000
χ574-4-44-222-204400-4-4-4-444-2-200002222-2-2000000004-4-44-222-20000000000000000000000000000000
χ584-4-44-222-204400-4-4-4-444-2-200002222-2-200000000-444-42-2-220000000000000000000000000000000
χ598888-4-4-4-482-4-4-42-4-422-4-1222-4-4-12-12-12-1-122-1-122000000000000000000000000000000000000000
χ608888-4-4-4-48-42-4-4-422-4-422-1-4-4222-12-12-122-1-122-1-1000000000000000000000000000000000000000
χ618888-4-4-4-4-82-4442-4-422-4-12-2-244-12-12-1211-2-211-2-2000000000000000000000000000000000000000
χ628888-4-4-4-4-8-4244-422-4-422-144-2-22-12-12-1-2-211-2-211000000000000000000000000000000000000000
χ6388-8-888-8-80-4200-42-244-2-420000-424-24-200000000000000000000000000000000000000000000000
χ6488-8-8-4-44402-4002-44-2-24-126-600-121-21-2-3300-3300000000000000000000000000000000000000000
χ6588-8-8-4-44402-4002-44-2-24-12-6600-121-21-23-3003-300000000000000000000000000000000000000000
χ6688-8-8-4-4440-4200-42-244-22-100002-1-21-2100−3i33i3003i3−3i3000000000000000000000000000000000000000
χ6788-8-8-4-4440-4200-42-244-22-100002-1-21-21003i3−3i300−3i33i3000000000000000000000000000000000000000
χ688-88-88-88-802-400-24-42-242-40000-242-4-2400000000000000000000000000000000000000000000000
χ698-88-88-88-80-42004-22-44-2-4200004-2-424-200000000000000000000000000000000000000000000000
χ708-88-8-44-4402-4−4i34i3-24-42-24-1200001-2-121-2−i3−i32i32i3i3i3−2i3−2i3000000000000000000000000000000000000000
χ718-88-8-44-4402-44i3−4i3-24-42-24-1200001-2-121-2i3i3−2i3−2i3−i3−i32i32i3000000000000000000000000000000000000000
χ728-88-8-44-440-42−4i34i34-22-44-22-10000-212-1-212i32i3−i3−i3−2i3−2i3i3i3000000000000000000000000000000000000000
χ738-88-8-44-440-424i3−4i34-22-44-22-10000-212-1-21−2i3−2i3i3i32i32i3−i3−i3000000000000000000000000000000000000000
χ748-8-888-8-8802-400-244-22-42-40000-24-242-400000000000000000000000000000000000000000000000
χ758-8-88-444-402-400-244-22-4-1200001-21-2-12−3i33i3003i3−3i300000000000000000000000000000000000000000
χ768-8-88-444-402-400-244-22-4-1200001-21-2-123i3−3i300−3i33i300000000000000000000000000000000000000000
χ778-8-88-444-40-42004-2-24-422-1006-6-21-212-100-3300-33000000000000000000000000000000000000000
χ788-8-88-444-40-42004-2-24-422-100-66-21-212-1003-3003-3000000000000000000000000000000000000000

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