Finite Group Databasebeta

← Group #72220560

Character table — Group #72220560

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11444444449999161616161616161618181818363636363636363636363636363636367272727272727272727272727272727272727272727272728181144144144144144144144144162162162162162162162162
order12333366662222333366664444222244446666666666666666121212121212121212121212121212122266661212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111
χ3111111111111111111111111-1-111-1-111-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1
χ51111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1
χ61111111111111111111111-1-111-1-11111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ91-11111-1-1-1-111-1-11111-1-1-1-1i−ii−i1-11-1i−ii−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-111-11-1i−ii−ii−ii−i11-1-1
χ101-11111-1-1-1-111-1-11111-1-1-1-1i−ii−i-11-11−ii−ii1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11-11−ii−iii−ii−i11-1-1
χ111-11111-1-1-1-111-1-11111-1-1-1-1i−i−ii1-1-11i−i−ii1111-1-1-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-111-1-11i−i−iii−i−ii-1-111
χ121-11111-1-1-1-111-1-11111-1-1-1-1i−i−ii-111-1−iii−i1111-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-11-111-1−iii−ii−i−ii-1-111
χ131-11111-1-1-1-111-1-11111-1-1-1-1−iii−i1-1-11−iii−i1111-1-1-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-111-1-11−iii−i−iii−i-1-111
χ141-11111-1-1-1-111-1-11111-1-1-1-1−iii−i-111-1i−i−ii1111-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-11-111-1i−i−ii−iii−i-1-111
χ151-11111-1-1-1-111-1-11111-1-1-1-1−ii−ii1-11-1−ii−ii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-111-11-1−ii−ii−ii−ii11-1-1
χ161-11111-1-1-1-111-1-11111-1-1-1-1−ii−ii-11-11i−ii−i1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11-11i−ii−i−ii−ii11-1-1
χ1722222222222-22-22222222200220000000022-2-222-2-2000000000000000000002222-2-20000000000-2-20000
χ1822222222222-22-22222222200-2-20000000022-2-222-2-200000000000000000000-2-2-2-2-2-20000000000220000
χ192222222222-22-2222222222220000000000-2-222-2-222000000000000000022220000-2-200000000-2-2000000
χ202222222222-22-2222222222-2-20000000000-2-222-2-2220000000000000000-2-2-2-20000-2-20000000022000000
χ212222222222-2-2-2-222222222000000000000-2-2-2-2-2-2-2-2000000000000000000000000220000000000002-22-2
χ222222222222-2-2-2-222222222000000000000-2-2-2-2-2-2-2-200000000000000000000000022000000000000-22-22
χ232-22222-2-2-2-22-2-222222-2-2-2-2002i−2i0000000022-2-2-2-222000000000000000000002i2i−2i−2i2-20000000000−2i2i0000
χ242-22222-2-2-2-22-2-222222-2-2-2-200−2i2i0000000022-2-2-2-22200000000000000000000−2i−2i2i2i2-200000000002i−2i0000
χ252-22222-2-2-2-2-222-22222-2-2-2-22i−2i0000000000-2-22222-2-200000000000000002i2i−2i−2i00002-200000000−2i2i000000
χ262-22222-2-2-2-2-222-22222-2-2-2-2−2i2i0000000000-2-22222-2-20000000000000000−2i−2i2i2i00002-2000000002i−2i000000
χ272-22222-2-2-2-2-2-2222222-2-2-2-2000000000000-2-2-2-22222000000000000000000000000-220000000000002-2-22
χ282-22222-2-2-2-2-2-2222222-2-2-2-2000000000000-2-2-2-22222000000000000000000000000-22000000000000-222-2
χ2944144-2144-204041-21-21-21-2440000220022001-2001-200002-12-100002-12-11-21-200000000-1-100-1-100000000
χ3044144-2144-204041-21-21-21-2440000-2-200-2-2001-2001-20000-21-210000-21-211-21-20000000011001100000000
χ3144144-2144-204041-21-21-21-2-4-400002200-2-2001-2001-200002-12-10000-21-21-12-1200000000-1-1001100000000
χ3244144-2144-204041-21-21-21-2-4-40000-2-20022001-2001-20000-21-2100002-12-1-12-12000000001100-1-100000000
χ334441-2441-2440401-2-21-211-20044220000221-2001-200-12-1200000000-12-1200001-21-200-1-10000-1-100000000
χ344441-2441-2440401-2-21-211-20044-2-20000-2-21-2001-2001-21-2000000001-21-200001-21-2001100001100000000
χ354441-2441-2440401-2-21-211-200-4-4220000-2-21-2001-200-12-12000000001-21-20000-12-1200-1-100001100000000
χ364441-2441-2440401-2-21-211-200-4-4-2-20000221-2001-2001-21-200000000-12-120000-12-1200110000-1-100000000
χ37444-2144-2144040-211-21-2-21004400222200-2100-21000000-12-12-12-1200000000-21-210000-1-1-1-10000000000
χ38444-2144-2144040-211-21-2-21004400-2-2-2-200-2100-210000001-21-21-21-200000000-21-21000011110000000000
χ39444-2144-2144040-211-21-2-2100-4-40022-2-200-2100-21000000-12-121-21-2000000002-12-10000-1-1110000000000
χ40444-2144-2144040-211-21-2-2100-4-400-2-22200-2100-210000001-21-2-12-12000000002-12-1000011-1-10000000000
χ4144-2441-24410404-21-21-21-2144002200220000-2100-212-12-100002-12-10000-21-21000000-1-100-1-10000000000
χ4244-2441-24410404-21-21-21-214400-2-200-2-20000-2100-21-21-210000-21-210000-21-210000001100110000000000
χ4344-2441-24410404-21-21-21-21-4-4002200-2-20000-2100-212-12-10000-21-2100002-12-1000000-1-100110000000000
χ4444-2441-24410404-21-21-21-21-4-400-2-200220000-2100-21-21-2100002-12-100002-12-10000001100-1-10000000000
χ454-4144-2-1-4-42040-41-21-2-12-124i−4i00002-2002i−2i001-200-1200002-1-2100002i−i−2iii−2i−i2i00000000-1100−ii00000000
χ464-4144-2-1-4-42040-41-21-2-12-124i−4i0000-2200−2i2i001-200-120000-212-10000−2ii2i−ii−2i−i2i000000001-100i−i00000000
χ474-4144-2-1-4-42040-41-21-2-12-12−4i4i00002-200−2i2i001-200-1200002-1-210000−2ii2i−i−i2ii−2i00000000-1100i−i00000000
χ484-4144-2-1-4-42040-41-21-2-12-12−4i4i0000-22002i−2i001-200-120000-212-100002i−i−2ii−i2ii−2i000000001-100−ii00000000
χ494-441-24-4-12-440-401-2-212-1-12004i−4i2-200002i−2i1-200-1200-121-200000000−i2ii−2i0000i−2i−i2i00-110000−ii00000000
χ504-441-24-4-12-440-401-2-212-1-12004i−4i-220000−2i2i1-200-12001-2-1200000000i−2i−i2i0000i−2i−i2i001-10000i−i00000000
χ514-441-24-4-12-440-401-2-212-1-1200−4i4i2-20000−2i2i1-200-1200-121-200000000i−2i−i2i0000−i2ii−2i00-110000i−i00000000
χ524-441-24-4-12-440-401-2-212-1-1200−4i4i-2200002i−2i1-200-12001-2-1200000000−i2ii−2i0000−i2ii−2i001-10000−ii00000000
χ534-44-214-42-1-440-40-211-2-122-1004i−4i002-22i−2i00-21002-1000000-121-2−i2ii−2i00000000−2ii2i−i0000-11−ii0000000000
χ544-44-214-42-1-440-40-211-2-122-1004i−4i00-22−2i2i00-21002-10000001-2-12i−2i−i2i00000000−2ii2i−i00001-1i−i0000000000
χ554-44-214-42-1-440-40-211-2-122-100−4i4i002-2−2i2i00-21002-1000000-121-2i−2i−i2i000000002i−i−2ii0000-11i−i0000000000
χ564-44-214-42-1-440-40-211-2-122-100−4i4i00-222i−2i00-21002-10000001-2-12−i2ii−2i000000002i−i−2ii00001-1−ii0000000000
χ574-4-24412-4-4-1040-4-21-212-12-14i−4i002-2002i−2i0000-21002-12-1-2100002i−i−2ii0000−2ii2i−i000000-1100−ii0000000000
χ584-4-24412-4-4-1040-4-21-212-12-14i−4i00-2200−2i2i0000-21002-1-212-10000−2ii2i−i0000−2ii2i−i0000001-100i−i0000000000
χ594-4-24412-4-4-1040-4-21-212-12-1−4i4i002-200−2i2i0000-21002-12-1-210000−2ii2i−i00002i−i−2ii000000-1100i−i0000000000
χ604-4-24412-4-4-1040-4-21-212-12-1−4i4i00-22002i−2i0000-21002-1-212-100002i−i−2ii00002i−i−2ii0000001-100−ii0000000000
χ6188288-4288-40-80-82-42-42-42-400000000000000-2400-24000000000000000000000000000000000000000000
χ628882-4882-48-80-802-4-42-422-4000000000000-2400-2400000000000000000000000000000000000000000000
χ63888-4288-428-80-80-422-42-4-420000000000004-2004-200000000000000000000000000000000000000000000
χ6488-4882-48820-80-8-42-42-42-42000000000000004-2004-2000000000000000000000000000000000000000000
χ658-8288-4-2-8-840-8082-42-4-24-2400000000000000-24002-4000000000000000000000000000000000000000000
χ668-882-48-8-24-8-80802-4-424-2-24000000000000-24002-400000000000000000000000000000000000000000000
χ678-88-428-84-2-8-8080-422-4-244-20000000000004-200-4200000000000000000000000000000000000000000000
χ688-8-48824-8-8-20-808-42-424-24-2000000000000004-200-42000000000000000000000000000000000000000000
χ69161644-8-844-8-8000014-2-2-2-21400000000004400000000000000000000-2-2-2-200000000000000001100000000
χ70161644-8-844-8-8000014-2-2-2-2140000000000-4-40000000000000000000022220000000000000000-1-100000000
χ7116164-84-84-84-80000-2-21414-2-2000000440000000000000000-2-2-2-20000000000000000000011000000000000
χ7216164-84-84-84-80000-2-21414-2-2000000-4-40000000000000000222200000000000000000000-1-1000000000000
χ731616-84-84-84-840000-2-24141-2-200004400000000000000-2-2-2-200000000000000000000001100000000000000
χ741616-84-84-84-840000-2-24141-2-20000-4-40000000000000022220000000000000000000000-1-100000000000000
χ751616-8-844-8-844000041-2-2-2-2410000000044000000000000000000-2-2-2-2000000000000000000110000000000
χ761616-8-844-8-844000041-2-2-2-24100000000-4-40000000000000000002222000000000000000000-1-10000000000
χ7716-1644-8-8-4-488000014-2-222-1-400000000004i−4i00000000000000000000−2i−2i2i2i0000000000000000i−i00000000
χ7816-1644-8-8-4-488000014-2-222-1-40000000000−4i4i000000000000000000002i2i−2i−2i0000000000000000−ii00000000
χ7916-164-84-8-48-480000-2-214-1-4220000004-40000000000000000-2-222000000000000000000001-1000000000000
χ8016-164-84-8-48-480000-2-214-1-422000000-44000000000000000022-2-200000000000000000000-11000000000000
χ8116-16-84-848-48-40000-2-241-4-12200004-400000000000000-2-22200000000000000000000001-100000000000000
χ8216-16-84-848-48-40000-2-241-4-1220000-440000000000000022-2-20000000000000000000000-1100000000000000
χ8316-16-8-84488-4-4000041-2-222-4-1000000004i−4i000000000000000000−2i−2i2i2i000000000000000000i−i0000000000
χ8416-16-8-84488-4-4000041-2-222-4-100000000−4i4i0000000000000000002i2i−2i−2i000000000000000000−ii0000000000

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