Finite Group Databasebeta

← Group #72310334

Character table — Group #72310334

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size112222222444444444444448888888888816161616161632323232323232323232323232323232323232323232323264646464646464646464646464646464
order12222222222222222222222222222222442224444444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1211111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1311111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1411111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1511111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222222-2-22-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222222222222-2-22-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ19222222222222222-2-2-2-2-2-2-2-22-2-222-222-2-2-2222-2-2-2000000000000000000000000000000002-22-20000
χ20222222222222222-2-2-2-2-2-2-2-22-2-222-222-2-2-2222-2-2-200000000000000000000000000000000-22-220000
χ21222222222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-222-2-2-22220000000000000000000000000000000000002-22-2
χ22222222222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-222-2-2-2222000000000000000000000000000000000000-22-22
χ2322222222222-2-2-2-222-2-222-2-22-2-2-2-22222-2-2-2-2222-20000000000000000000000000000000000002i−2i−2i2i
χ2422222222222-2-2-2-222-2-222-2-22-2-2-2-22222-2-2-2-2222-2000000000000000000000000000000000000−2i2i2i−2i
χ2522222222222-2-2-2-222-2-222-2-22-2-2-2-22-2-222222-2-2-22000000000000000000000000000000002i−2i−2i2i0000
χ2622222222222-2-2-2-222-2-222-2-22-2-2-2-22-2-222222-2-2-2200000000000000000000000000000000−2i2i2i−2i0000
χ2722222222222-2-2-2-2-2-222-2-222222-2-2-222-222-2-22-2-220000000022-2-2-2-222000000000000000000000000
χ2822222222222-2-2-2-2-2-222-2-222222-2-2-222-222-2-22-2-2200000000-2-22222-2-2000000000000000000000000
χ29222222222-2-222-2-222222222-2-2-22-2-222-2-2-22-2-22-220000000000000000000000002-2002-20000000000
χ30222222222-2-222-2-222222222-2-2-22-2-222-2-2-22-2-22-22000000000000000000000000-2200-220000000000
χ31222222222-2-222-2-222222222-2-2-22-2-2-2-2-222-222-22-2000000000000000000000000002-2002-200000000
χ32222222222-2-222-2-222222222-2-2-22-2-2-2-2-222-222-22-200000000000000000000000000-2200-2200000000
χ33222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-22222222-2-2-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ34222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-22222222-2-2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ35222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-22-2-22-2-2-2222-22000000000000000022-2-222-2-20000000000000000
χ36222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-22-2-22-2-2-2222-220000000000000000-2-222-2-2220000000000000000
χ37222222222-2-2-2-22222-2-222-2-2-222-22-222-222-22-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ38222222222-2-2-2-22222-2-222-2-2-222-22-222-222-22-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ39222222222-2-2-2-22222-2-222-2-2-222-22-2-2-2-2-2-22-22-22222-2-2-2-22200000000000000000000000000000000
χ40222222222-2-2-2-22222-2-222-2-2-222-22-2-2-2-2-2-22-22-222-2-22222-2-200000000000000000000000000000000
χ41222222222-2-2-2-222-2-222-2-222-2-2-2-222222-2-2-22-2-222000000000000000000000000002-200-2200000000
χ42222222222-2-2-2-222-2-222-2-222-2-2-2-222222-2-2-22-2-22200000000000000000000000000-22002-200000000
χ43222222222-2-2-2-222-2-222-2-222-2-2-2-222-2-22222-222-2-20000000000000000000000002-200-220000000000
χ44222222222-2-2-2-222-2-222-2-222-2-2-2-222-2-22222-222-2-2000000000000000000000000-22002-20000000000
χ4544444-4-4-4-4000044004-4004-40000-4400-40000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4644444-4-4-4-4000044004-4004-40000-4400-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4744444-4-4-4-400004400-4400-440000-4-40040000000000000000000000002-2-22-222-20000000000000000
χ4844444-4-4-4-400004400-4400-440000-4-4004000000000000000000000000-222-22-2-220000000000000000
χ4944444-4-4-4-40000-4-4004-4004-400004-40040000000000000000000000002-22-2-22-220000000000000000
χ5044444-4-4-4-40000-4-4004-4004-400004-4004000000000000000000000000-22-222-22-20000000000000000
χ5144444-4-4-4-40000-4-400-4400-4400004400-40000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5244444-4-4-4-40000-4-400-4400-4400004400-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ53444-4-444-4-400440044-44-4-44-4000-400000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ54444-4-444-4-400440044-44-4-44-4000-40000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ55444-4-444-4-4004400-4-44-444-44000-400000000000002-2-222-2-2200000000000000000000000000000000
χ56444-4-444-4-4004400-4-44-444-44000-40000000000000-222-2-222-200000000000000000000000000000000
χ57444-4-444-4-400-4-400444-4-4-4-44000400000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ58444-4-444-4-400-4-400444-4-4-4-4400040000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ59444-4-444-4-400-4-400-4-4-44444-4000400000000000002-22-2-22-2200000000000000000000000000000000
χ60444-4-444-4-400-4-400-4-4-44444-400040000000000000-22-222-22-200000000000000000000000000000000
χ61444-4-4-4-444440000004400-4-4-44-4000000000000000000000000004i−4i00000000000000000000000000
χ62444-4-4-4-444440000004400-4-4-44-400000000000000000000000000−4i4i00000000000000000000000000
χ63444-4-4-4-44444000000-4-40044-4-440000000000000000000000004-40000000000000000000000000000
χ64444-4-4-4-44444000000-4-40044-4-44000000000000000000000000-440000000000000000000000000000
χ65444-4-4-4-444-4-40000004400-4-44-4400000000000000000000000000004i−4i000000000000000000000000
χ66444-4-4-4-444-4-40000004400-4-44-440000000000000000000000000000−4i4i000000000000000000000000
χ67444-4-4-4-444-4-4000000-4-4004444-400000000000000000000004-4000000000000000000000000000000
χ68444-4-4-4-444-4-4000000-4-4004444-40000000000000000000000-44000000000000000000000000000000
χ6988-88-88-88-8000000000000000000000008-80000000000000000000000000000000000000000000000
χ7088-88-88-88-800000000000000000000000-880000000000000000000000000000000000000000000000
χ7188-88-8-88-880000008-8008-800000000000000000000000000000000000000000000000000000000000
χ7288-88-8-88-88000000-8800-8800000000000000000000000000000000000000000000000000000000000
χ7388-8-888-8-88000000000000000000008-80000000000000000000000000000000000000000000000000
χ7488-8-888-8-8800000000000000000000-880000000000000000000000000000000000000000000000000
χ7588-8-88-888-80000008-800-8800000000000000000000000000000000000000000000000000000000000
χ7688-8-88-888-8000000-88008-800000000000000000000000000000000000000000000000000000000000
χ7716-1600000008-88-88-800000000000000000000000000000000000000000000000000000000000000000
χ7816-1600000008-8-88-8800000000000000000000000000000000000000000000000000000000000000000
χ7916-160000000-888-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8016-160000000-88-888-800000000000000000000000000000000000000000000000000000000000000000

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