Finite Group Databasebeta

← Group #72285859

Character table — Group #72285859

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222224444444444888888888888888881616161616161616161616161616161616161616323232323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222224444444444444444444444444444224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-111-11111-1-1-1-1
χ911111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-111-1-1-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i
χ1011111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-111−i−iii−i−iii
χ1111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-111-1-1-1-111−i−i−i−iiiii1-11-1ii−i−i−i−iii
χ1211111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-111-1-111−i−i−i−iiiii-11-11−i−iiiii−i−i
χ1311111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii
χ1411111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i
χ1511111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-111-1-1-1-111iiii−i−i−i−i1-11-1−i−iiiii−i−i
χ1611111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-111-1-111iiii−i−i−i−i-11-11ii−i−i−i−iii
χ172222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000202022000000-2-2-2-200000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-20-20-2-2000000222200000000000000000000
χ1922222222222-2-2222-2-22222-2-2-2-2-2-222222222-2-2-2-200000000000000002020-2-2000000-2-22200000000000000000000
χ2022222222222-2-2222-2-22222-2-2-2-2-2-222222222-2-2-2-20000000000000000-20-202200000022-2-200000000000000000000
χ21222222222-2-222222-2-22-2-2-222-2-2-2222-2-222-2-2-2-22200000000000000000202000000-2-2000000000000-200200000000
χ22222222222-2-222222-2-22-2-2-222-2-2-2222-2-222-2-2-2-22200000000000000000-20-200000022000000000000200-200000000
χ23222222222-2-222222-2-22-2-2-222-2-2-22-2-222-2-22222-2-2000000000000000000000022-2-2000000000000000-22000000000
χ24222222222-2-222222-2-22-2-2-222-2-2-22-2-222-2-22222-2-20000000000000000000000-2-2220000000000000002-2000000000
χ25222222222-2-2-2-2222222-2-2-2-2-2222-222-2-222-2-222-2-200000000000000000000002222000000000000000-2-2000000000
χ26222222222-2-2-2-2222222-2-2-2-2-2222-222-2-222-2-222-2-20000000000000000000000-2-2-2-200000000000000022000000000
χ27222222222-2-2-2-2222222-2-2-2-2-2222-2-2-222-2-222-2-2220000000000000000020200000022000000000000-200-200000000
χ28222222222-2-2-2-2222222-2-2-2-2-2222-2-2-222-2-222-2-22200000000000000000-20-2000000-2-2000000000000200200000000
χ29222-222-2-2-2220022-200-22-2-20000002i−2i2i−2i2i−2i2i−2i00001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i20-2000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ30222-222-2-2-2220022-200-22-2-20000002i−2i2i−2i2i−2i2i−2i00001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i-20200000000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ31222-222-2-2-2220022-200-22-2-20000002i−2i2i−2i2i−2i2i−2i0000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i20-2000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ32222-222-2-2-2220022-200-22-2-20000002i−2i2i−2i2i−2i2i−2i0000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i-20200000000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ33222-222-2-2-2220022-200-22-2-2000000−2i2i−2i2i−2i2i−2i2i00001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i20-200000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ34222-222-2-2-2220022-200-22-2-2000000−2i2i−2i2i−2i2i−2i2i00001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i-202000000000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ35222-222-2-2-2220022-200-22-2-2000000−2i2i−2i2i−2i2i−2i2i0000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i20-200000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ36222-222-2-2-2220022-200-22-2-2000000−2i2i−2i2i−2i2i−2i2i0000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i-202000000000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3722-222-22-2-2-2-2002-2200-222-20000002i−2i−2i2i−2i2i2i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002-20000002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3822-222-22-2-2-2-2002-2200-222-20000002i−2i−2i2i−2i2i2i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000-22000000−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3922-222-22-2-2-2-2002-2200-222-20000002i−2i−2i2i−2i2i2i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002-20000002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4022-222-22-2-2-2-2002-2200-222-20000002i−2i−2i2i−2i2i2i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000-22000000−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4122-222-22-2-2-2-2002-2200-222-2000000−2i2i2i−2i2i−2i−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002-2000000−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4222-222-22-2-2-2-2002-2200-222-2000000−2i2i2i−2i2i−2i−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000-220000002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4322-222-22-2-2-2-2002-2200-222-2000000−2i2i2i−2i2i−2i−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002-2000000−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4422-222-22-2-2-2-2002-2200-222-2000000−2i2i2i−2i2i−2i−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000-220000002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4522-2-22-2-22222222-2-2222-22-22-22-2-2-22222-2-2-2-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ4622-2-22-2-22222222-2-2222-22-22-22-2-2-22222-2-2-2-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4722-2-22-2-22222222-2-2222-22-22-22-2-2-2-2-2-2-22222-22-22000000000000000000000000000000000000000000002-22-20000
χ4822-2-22-2-22222222-2-2222-22-22-22-2-2-2-2-2-2-22222-22-2200000000000000000000000000000000000000000000-22-220000
χ4922-2-22-2-22222-2-22-2-2-2-22-22-2-22-22222222-2-2-2-2-22-22000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5022-2-22-2-22222-2-22-2-2-2-22-22-2-22-22222222-2-2-2-2-22-2200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5122-2-22-2-22222-2-22-2-2-2-22-22-2-22-2222-2-2-2-222222-22-20000000000000000000000000000000000000000000000002-2-22
χ5222-2-22-2-22222-2-22-2-2-2-22-22-2-22-2222-2-2-2-222222-22-2000000000000000000000000000000000000000000000000-222-2
χ5322-2-22-2-222-2-2222-2-2-2-222-222-2-222-222-2-2-2-222-222-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ5422-2-22-2-222-2-2222-2-2-2-222-222-2-222-222-2-2-2-222-222-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ5522-2-22-2-222-2-2222-2-2-2-222-222-2-222-2-2-22222-2-22-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ5622-2-22-2-222-2-2222-2-2-2-222-222-2-222-2-2-22222-2-22-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ5722-2-22-2-222-2-2-2-22-2-22222-22-222-2-2222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ5822-2-22-2-222-2-2-2-22-2-22222-22-222-2-2222-2-2-2-2222-2-22-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ5922-2-22-2-222-2-2-2-22-2-22222-22-222-2-22-2-22222-2-2-222-2000000000000000000000000000000002-2-222-2-22000000000000
χ6022-2-22-2-222-2-2-2-22-2-22222-22-222-2-22-2-22222-2-2-222-200000000000000000000000000000000-222-2-222-2000000000000
χ614444444440000-4-4-444-400000-44-400000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ624444444440000-4-4-444-400000-44-40000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ634444444440000-4-4-4-4-4-4000004-4400000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ644444444440000-4-4-4-4-4-4000004-440000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ65444-444-4-4-40044-4-44004000-44000-40000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ66444-444-4-4-40044-4-44004000-44000-4000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ67444-444-4-4-400-4-4-4-440040004-400040000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000000000
χ68444-444-4-4-400-4-4-4-440040004-40004000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000000000
χ69444-444-4-4-4-4-40044-400-4-4440000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ70444-444-4-4-4-4-40044-400-4-444000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7144-444-44-4-40044-44-4004000-4-400040000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ7244-444-44-4-40044-44-4004000-4-40004000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ7344-444-44-4-400-4-4-44-400400044000-40000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ7444-444-44-4-400-4-4-44-400400044000-4000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ7544-444-44-4-444004-4400-4-4-440000004i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ7644-444-44-4-444004-4400-4-4-44000000−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7744-4-44-4-4440000-44444-400000-4-4400000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ7844-4-44-4-4440000-44444-400000-4-440000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ7944-4-44-4-4440000-444-4-4-40000044-400000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ8044-4-44-4-4440000-444-4-4-40000044-40000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ818888-8-8-88-800000000000000000000000000000000000000000000000000000004i−4i00000000000000000000000000
χ828888-8-8-88-80000000000000000000000000000000000000000000000000000000−4i4i00000000000000000000000000
χ83888-8-8-88-880000000000000000000000000000000000000000000000000000000004-4000000000000000000000000
χ84888-8-8-88-88000000000000000000000000000000000000000000000000000000000-44000000000000000000000000
χ8588-88-88-8-8800000000000000000000000000000000000000000000000040-400000000000000000000000000000000
χ8688-88-88-8-88000000000000000000000000000000000000000000000000-40400000000000000000000000000000000
χ8788-8-8-8888-8000000000000000000000000000000000000000000000000000004-40000000000000000000000000000
χ8888-8-8-8888-800000000000000000000000000000000000000000000000000000-440000000000000000000000000000
χ8916-1600000008-88-80008-800000000000000000000000000000000000000000000000000000000000000000000000000
χ9016-1600000008-8-88000-8800000000000000000000000000000000000000000000000000000000000000000000000000
χ9116-160000000-888-8000-8800000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-160000000-88-880008-800000000000000000000000000000000000000000000000000000000000000000000000000

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