Finite Group Databasebeta

← Group #72270554

Character table — Group #72270554

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222224444444444444888888888888888121212121212121212121212121212121616161616161616161616161616161616161616242424242424242432323232323232324848484848484848
order122223444466668888121212122424448816161616161616162424242244444488888888444444881212242448484848484848481616161616161616121212121212242422244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ9111111111111111111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1
χ1711-1-111-111-11-1-1111-1-1-111-1111-11-1ii−i−iii−i−i1-1-11-11-111-1-111-1-111-1-1i−i1-11-1i−i1-11-1ii−i−iii−i−iii−i−iii−i−ii−i1-11-1i−i1-11-1i−ii−i
χ1811-1-111-111-11-1-1111-1-1-111-1111-11-1ii−i−iii−i−i1-1-11-11-111-1-111-1-111-1-1−ii-11-11−ii1-11-1ii−i−iii−i−iii−i−iii−i−i−ii-11-11−ii-11-11−ii−ii
χ1911-1-111-111-11-1-1111-1-1-111-1111-11-1ii−i−iii−i−i1-1-1-11-11-1-111-1-111-1-111i−i1-11-1i−i1-11-1ii−i−iii−i−i−i−iii−i−iiii−i1-11-1i−i-11-11−ii−ii
χ2011-1-111-111-11-1-1111-1-1-111-1111-11-1ii−i−iii−i−i1-1-1-11-11-1-111-1-111-1-111−ii-11-11−ii1-11-1ii−i−iii−i−i−i−iii−i−iii−ii-11-11−ii1-11-1i−ii−i
χ2111-1-111-111-11-1-1111-1-1-111-1111-11-1−i−iii−i−iii1-1-11-11-111-1-111-1-111-1-1i−i-11-11i−i1-11-1−i−iii−i−iii−i−iii−i−iiii−i-11-11i−i-11-11i−ii−i
χ2211-1-111-111-11-1-1111-1-1-111-1111-11-1−i−iii−i−iii1-1-11-11-111-1-111-1-111-1-1−ii1-11-1−ii1-11-1−i−iii−i−iii−i−iii−i−iii−ii1-11-1−ii1-11-1−ii−ii
χ2311-1-111-111-11-1-1111-1-1-111-1111-11-1−i−iii−i−iii1-1-1-11-11-1-111-1-111-1-111i−i-11-11i−i1-11-1−i−iii−i−iiiii−i−iii−i−ii−i-11-11i−i1-11-1−ii−ii
χ2411-1-111-111-11-1-1111-1-1-111-1111-11-1−i−iii−i−iii1-1-1-11-11-1-111-1-111-1-111−ii1-11-1−ii1-11-1−i−iii−i−iiiii−i−iii−i−i−ii1-11-1−ii-11-11i−ii−i
χ2511-1-111-111-11-1-1111-1-1-111-111-11-11ii−i−i−i−iii1-1-11-11-1-1-11111-1-1-1-111i−i1-1-11−ii-11-11ii−i−i−i−iiiii−i−i−i−iiii−i1-1-11−ii1-1-11i−i−ii
χ2611-1-111-111-11-1-1111-1-1-111-111-11-11ii−i−i−i−iii1-1-11-11-1-1-11111-1-1-1-111−ii-111-1i−i-11-11ii−i−i−i−iiiii−i−i−i−iii−ii-111-1i−i-111-1−iii−i
χ2711-1-111-111-11-1-1111-1-1-111-111-11-11ii−i−i−i−iii1-1-1-11-1111-1-1-1-11111-1-1i−i1-1-11−ii-11-11ii−i−i−i−iii−i−iiiii−i−ii−i1-1-11−ii-111-1−iii−i
χ2811-1-111-111-11-1-1111-1-1-111-111-11-11ii−i−i−i−iii1-1-1-11-1111-1-1-1-11111-1-1−ii-111-1i−i-11-11ii−i−i−i−iii−i−iiiii−i−i−ii-111-1i−i1-1-11i−i−ii
χ2911-1-111-111-11-1-1111-1-1-111-111-11-11−i−iiiii−i−i1-1-11-11-1-1-11111-1-1-1-111i−i-111-1−ii-11-11−i−iiiii−i−i−i−iiiii−i−ii−i-111-1−ii-111-1i−i−ii
χ3011-1-111-111-11-1-1111-1-1-111-111-11-11−i−iiiii−i−i1-1-11-11-1-1-11111-1-1-1-111−ii1-1-11i−i-11-11−i−iiiii−i−i−i−iiiii−i−i−ii1-1-11i−i1-1-11−iii−i
χ3111-1-111-111-11-1-1111-1-1-111-111-11-11−i−iiiii−i−i1-1-1-11-1111-1-1-1-11111-1-1i−i-111-1−ii-11-11−i−iiiii−i−iii−i−i−i−iiii−i-111-1−ii1-1-11−iii−i
χ3211-1-111-111-11-1-1111-1-1-111-111-11-11−i−iiiii−i−i1-1-1-11-1111-1-1-1-11111-1-1−ii1-1-11i−i-11-11−i−iiiii−i−iii−i−i−i−iii−ii1-1-11i−i-111-1i−i−ii
χ3322222222222222-2-2-2-22222-2-222-2-200000000-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-200000000000000000000000000000000
χ3422222222222222-2-2-2-22222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-2-2222222220000000022-2-200000000000000000000000000000000
χ3522222222222222-2-2-2-22222-2-2-2-22200000000-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-22200000000000000000000000000000000
χ3622222222222222-2-2-2-22222-2-2-2-22200000000-2-2-2-2-2-2-222222222-2-2-2-200000000-2-22200000000000000000000000000000000
χ3722222-12222-1-1-1-12222-1-1-1-1-1-1222222222222-1-1-1000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000
χ3822222-12222-1-1-1-12222-1-1-1-1-1-1222222222222-1-1-10000000000000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000001111111100000000
χ3922222-12222-1-1-1-12222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1000000000000000022-2-2-2-222-1-1-1-11111111100000000-1-11111-1-100000000
χ4022222-12222-1-1-1-12222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-10000000000000000-2-22222-2-2-1-1-1-1111111110000000011-1-1-1-11100000000
χ4122222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-100000000000000002222-2-2-2-21111-1-1-1-1111100000000-1-1-1-1111100000000
χ4222222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-10000000000000000-2-2-2-222221111-1-1-1-11111000000001111-1-1-1-100000000
χ4322222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1000000000000000022-2-222-2-211111111-1-1-1-100000000-1-111-1-11100000000
χ4422222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-10000000000000000-2-222-2-22211111111-1-1-1-10000000011-1-111-1-100000000
χ45222-2-2222-2-22-22-22-22-2-22-222200002i−2i2i−2i0000-22-200002i−2i2i−2i00002i−2i2i−2i0000000000002i−2i2i−2i000000002-22-20000000000000000
χ46222-2-2222-2-22-22-22-22-2-22-222200002i−2i2i−2i0000-22-20000−2i2i−2i2i0000−2i2i−2i2i0000000000002i−2i2i−2i00000000-22-220000000000000000
χ47222-2-2222-2-22-22-22-22-2-22-22220000−2i2i−2i2i0000-22-200002i−2i2i−2i00002i−2i2i−2i000000000000−2i2i−2i2i00000000-22-220000000000000000
χ48222-2-2222-2-22-22-22-22-2-22-22220000−2i2i−2i2i0000-22-20000−2i2i−2i2i0000−2i2i−2i2i000000000000−2i2i−2i2i000000002-22-20000000000000000
χ49222-2-2222-2-22-22-2-22-22-22-22-2-2000000002i−2i2i−2i2-2200002i−2i2i−2i0000−2i2i−2i2i00000000000000002i−2i2i−2i2-22-200000000000000000000
χ50222-2-2222-2-22-22-2-22-22-22-22-2-2000000002i−2i2i−2i2-220000−2i2i−2i2i00002i−2i2i−2i00000000000000002i−2i2i−2i-22-2200000000000000000000
χ51222-2-2222-2-22-22-2-22-22-22-22-2-200000000−2i2i−2i2i2-2200002i−2i2i−2i0000−2i2i−2i2i0000000000000000−2i2i−2i2i-22-2200000000000000000000
χ52222-2-2222-2-22-22-2-22-22-22-22-2-200000000−2i2i−2i2i2-220000−2i2i−2i2i00002i−2i2i−2i0000000000000000−2i2i−2i2i2-22-200000000000000000000
χ5322-22-22-22-2222-2-22-2-2222-2-22200002-2-220000-2-2200002i−2i−2i2i00002i−2i−2i2i0000000000002-2-2200000000−2i2i2i−2i0000000000000000
χ5422-22-22-22-2222-2-22-2-2222-2-22200002-2-220000-2-220000−2i2i2i−2i0000−2i2i2i−2i0000000000002-2-22000000002i−2i−2i2i0000000000000000
χ5522-22-22-22-2222-2-22-2-2222-2-2220000-222-20000-2-2200002i−2i−2i2i00002i−2i−2i2i000000000000-222-2000000002i−2i−2i2i0000000000000000
χ5622-22-22-22-2222-2-22-2-2222-2-2220000-222-20000-2-220000−2i2i2i−2i0000−2i2i2i−2i000000000000-222-200000000−2i2i2i−2i0000000000000000
χ5722-22-22-22-2222-2-2-222-222-2-2-2-2000000002-2-2222-200002i−2i−2i2i0000−2i2i2i−2i00000000000000002-2-22−2i2i2i−2i00000000000000000000
χ5822-22-22-22-2222-2-2-222-222-2-2-2-2000000002-2-2222-20000−2i2i2i−2i00002i−2i−2i2i00000000000000002-2-222i−2i−2i2i00000000000000000000
χ5922-22-22-22-2222-2-2-222-222-2-2-2-200000000-222-222-200002i−2i−2i2i0000−2i2i2i−2i0000000000000000-222-22i−2i−2i2i00000000000000000000
χ6022-22-22-22-2222-2-2-222-222-2-2-2-200000000-222-222-20000−2i2i2i−2i00002i−2i−2i2i0000000000000000-222-2−2i2i2i−2i00000000000000000000
χ6122-2-222-222-22-2-22-2-222-222-2-2-22-2-2200000000-2222-22-222-2-2-2-222-2-222000000002-2-2200000000000000000000000000000000
χ6222-2-222-222-22-2-22-2-222-222-2-2-22-2-2200000000-222-22-22-2-22222-2-222-2-2000000002-2-2200000000000000000000000000000000
χ6322-2-222-222-22-2-22-2-222-222-2-2-2-222-200000000-2222-22-2-2-222-2-22222-2-200000000-222-200000000000000000000000000000000
χ6422-2-222-222-22-2-22-2-222-222-2-2-2-222-200000000-222-22-2222-2-222-2-2-2-22200000000-222-200000000000000000000000000000000
χ6522-2-22-1-222-2-111-122-2-21-1-11-1-12-22-22i2i−2i−2i2i2i−2i−2i-11100000000000000002i−2i2-22-22i−2i-11-11−i−iii−i−iii00000000−ii-11-11−ii00000000
χ6622-2-22-1-222-2-111-122-2-21-1-11-1-12-22-22i2i−2i−2i2i2i−2i−2i-1110000000000000000−2i2i-22-22−2i2i-11-11−i−iii−i−iii00000000i−i1-11-1i−i00000000
χ6722-2-22-1-222-2-111-122-2-21-1-11-1-12-22-2−2i−2i2i2i−2i−2i2i2i-11100000000000000002i−2i-22-222i−2i-11-11ii−i−iii−i−i00000000−ii1-11-1−ii00000000
χ6822-2-22-1-222-2-111-122-2-21-1-11-1-12-22-2−2i−2i2i2i−2i−2i2i2i-1110000000000000000−2i2i2-22-2−2i2i-11-11ii−i−iii−i−i00000000i−i-11-11i−i00000000
χ6922-2-22-1-222-2-111-122-2-21-1-11-1-1-22-222i2i−2i−2i−2i−2i2i2i-11100000000000000002i−2i2-2-22−2i2i1-11-1−i−iiiii−i−i00000000−ii-111-1i−i00000000
χ7022-2-22-1-222-2-111-122-2-21-1-11-1-1-22-222i2i−2i−2i−2i−2i2i2i-1110000000000000000−2i2i-222-22i−2i1-11-1−i−iiiii−i−i00000000i−i1-1-11−ii00000000
χ7122-2-22-1-222-2-111-122-2-21-1-11-1-1-22-22−2i−2i2i2i2i2i−2i−2i-11100000000000000002i−2i-222-2−2i2i1-11-1ii−i−i−i−iii00000000−ii1-1-11i−i00000000
χ7222-2-22-1-222-2-111-122-2-21-1-11-1-1-22-22−2i−2i2i2i2i2i−2i−2i-1110000000000000000−2i2i2-2-222i−2i1-11-1ii−i−i−i−iii00000000i−i-111-1−ii00000000
χ73444444-4-4-4-444440000-4-4-4-4000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-444440000-4-4-4-400000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ7544444-24444-2-2-2-2-4-4-4-4-2-2-2-22244-4-400000000222000000000000000000000000-2-22200000000000000000000000000000000
χ7644444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-4440000000022200000000000000000000000022-2-200000000000000000000000000000000
χ77444-4-44-4-4444-44-400004-44-400000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ78444-4-44-4-4444-44-400004-44-40000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ79444-4-4-244-4-4-22-224-44-42-22-2-2-200004i−4i4i−4i00002-220000000000000000000000000000−2i2i−2i2i0000000000000000000000000000
χ80444-4-4-244-4-4-22-224-44-42-22-2-2-20000−4i4i−4i4i00002-2200000000000000000000000000002i−2i2i−2i0000000000000000000000000000
χ81444-4-4-244-4-4-22-22-44-442-22-222000000004i−4i4i−4i-22-200000000000000000000000000000000−2i2i−2i2i000000000000000000000000
χ82444-4-4-244-4-4-22-22-44-442-22-22200000000−4i4i−4i4i-22-2000000000000000000000000000000002i−2i2i−2i000000000000000000000000
χ8344-44-444-44-444-4-40000-4-44400000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ8444-44-444-44-444-4-40000-4-4440000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ8544-44-4-2-44-44-2-2224-4-44-2-222-2-200004-4-44000022-20000000000000000000000000000-222-20000000000000000000000000000
χ8644-44-4-2-44-44-2-2224-4-44-2-222-2-20000-444-4000022-200000000000000000000000000002-2-220000000000000000000000000000
χ8744-44-4-2-44-44-2-222-444-4-2-22222000000004-4-44-2-2200000000000000000000000000000000-222-2000000000000000000000000
χ8844-44-4-2-44-44-2-222-444-4-2-2222200000000-444-4-2-22000000000000000000000000000000002-2-22000000000000000000000000
χ8944-4-4444-4-444-4-4400004-4-440000000000000000044-4-400000000000000000000000000000000000000000000000000000000
χ9044-4-4444-4-444-4-4400004-4-4400000000000000000-4-44400000000000000000000000000000000000000000000000000000000
χ9144-4-44-2-444-4-222-2-4-4442-2-22224-4-44000000002-2-2000000000000000000000000-222-200000000000000000000000000000000
χ9244-4-44-2-444-4-222-2-4-4442-2-2222-444-4000000002-2-20000000000000000000000002-2-2200000000000000000000000000000000
χ9388888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000000000000000
χ94888-8-8-4-8-888-44-440000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000
χ9588-88-8-48-88-8-4-444000044-4-400000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-88-48-8-88-444-40000-444-400000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-16000-8000080000000000046−46000000000000000000000000000000000000000000000000000000000000000000000000000
χ9916-16000-80000800000000000−4646000000000000000000000000000000000000000000000000000000000000000000000000000

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