Finite Group Databasebeta

← Group #72312503

Character table — Group #72312503

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1122222224444444444888888888888888881616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232646464646464
order12222222222222244442222222222244444422224444444444444444444444444444244444444444444444444488888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ11111111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ12111111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ13111111111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ14111111111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ15111111111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ16111111111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ171111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−iii−i−i11-1-111-1-111-1-11-11-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−iii−i−i1-1i−ii−i
χ181111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−iii−i−i11-1-111-1-111-1-1-11-11−iii−i−ii-1-111−i−iii-1-111ii−i−iii−i−i-11−ii−ii
χ191111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii−i−iii11-1-111-1-111-1-11-11-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii−i−iii1-1−ii−ii
χ201111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii−i−iii11-1-111-1-111-1-1-11-11i−i−iii−i-1-111ii−i−i-1-111−i−iii−i−iii-11i−ii−i
χ211111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1-1-1-1111-11ii−i−iii−i−iii−i−i11-1-1-1-111-1-1111-11-1i−ii−ii−i11-1-1ii−i−i-1-111−i−iii−i−iii-11−ii−ii
χ221111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1-1-1-1111-11ii−i−iii−i−iii−i−i11-1-1-1-111-1-111-11-11−iii−i−ii-1-111−i−iii11-1-1−i−iii−i−iii1-1i−ii−i
χ231111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1-1-1-1111-11−i−iii−i−iii−i−iii11-1-1-1-111-1-1111-11-1−ii−ii−ii11-1-1−i−iii-1-111ii−i−iii−i−i-11i−ii−i
χ241111-1-1-1-11111-1-1111-1-111-1-1-111-1-11-1111-1-1-1-1-1-1111-11−i−iii−i−iii−i−iii11-1-1-1-111-1-111-11-11i−i−iii−i-1-111ii−i−i11-1-1ii−i−iii−i−i1-1−ii−ii
χ251111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-111-11-1-1-11ii−i−iii−i−i−i−iii-1-11111-1-1-1-1111-11-1i−i−iii−i-1-111−i−iii11-1-1ii−i−i−i−iii-11−iii−i
χ261111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-111-11-1-1-11ii−i−iii−i−i−i−iii-1-11111-1-1-1-111-11-11−ii−ii−ii11-1-1ii−i−i-1-111ii−i−i−i−iii1-1i−i−ii
χ271111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-111-11-1-1-11−i−iii−i−iiiii−i−i-1-11111-1-1-1-1111-11-1−iii−i−ii-1-111ii−i−i11-1-1−i−iiiii−i−i-11i−i−ii
χ281111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-111-11-1-1-11−i−iii−i−iiiii−i−i-1-11111-1-1-1-111-11-11i−ii−ii−i11-1-1−i−iii-1-111−i−iiiii−i−i1-1−iii−i
χ291111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-1-1-11-1111-1ii−i−iii−i−i−i−iii-1-111-1-11111-1-11-11-1i−i−iii−i-1-111−i−iii-1-111−i−iiiii−i−i1-1i−i−ii
χ301111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-1-1-11-1111-1ii−i−iii−i−i−i−iii-1-111-1-11111-1-1-11-11−ii−ii−ii11-1-1ii−i−i11-1-1−i−iiiii−i−i-11−iii−i
χ311111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-1-1-11-1111-1−i−iii−i−iiiii−i−i-1-111-1-11111-1-11-11-1−iii−i−ii-1-111ii−i−i-1-111ii−i−i−i−iii1-1−iii−i
χ321111-1-1-1-11111-1-1111-1-111-1-1-1-1-1111-11-1-111-1-1-11-1111-1−i−iii−i−iiiii−i−i-1-111-1-11111-1-1-11-11i−ii−ii−i11-1-1−i−iii11-1-1ii−i−i−i−iii-11i−i−ii
χ33222222222222222-2-2-2-2-2-222-22-22-22-2-22-22-2-2000000000000000000002-22-20000000022-2-20000002-22-20000000000000000000000
χ34222222222222222-2-2-2-2-2-222-22-22-22-2-22-22-2-2000000000000000000002-22-200000000-2-222000000-22-220000000000000000000000
χ35222222222222222-2-2-2-2-2-222-2-22-222-2-2-22-22-200000000000000000000-22-220000000022-2-2000000-22-220000000000000000000000
χ36222222222222222-2-2-2-2-2-222-2-22-222-2-2-22-22-200000000000000000000-22-2200000000-2-2220000002-22-20000000000000000000000
χ372222222222-2-2-2-222222-2-22-2-20000-2-2200002220022002-22-22-22-200000000-2-2-2-2000000000000000000000000002-22-20000000000
χ382222222222-2-2-2-222222-2-22-2-20000-2-220000222002200-22-22-22-2200000000-2-2-2-200000000000000000000000000-22-220000000000
χ392222222222-2-2-2-222222-2-22-2-20000-2-2200002-2-200-2-2002-22-22-22-200000000222200000000000000000000000000-22-220000000000
χ402222222222-2-2-2-222222-2-22-2-20000-2-2200002-2-200-2-200-22-22-22-22000000002222000000000000000000000000002-22-20000000000
χ41222222222-22222-222222-2-2-222222-2-2-22222-2000000002222-2-2-2-2-2-2-2-2-2-2-2-200000000000000220000000000000000000000000000
χ42222222222-22222-222222-2-2-222222-2-2-22222-200000000-2-2-2-222222222-2-2-2-200000000000000-2-20000000000000000000000000000
χ43222222222-22222-222222-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-22222222200000000000000-2-20000000000000000000000000000
χ44222222222-22222-222222-2-2-22-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-2-2-2-2222200000000000000220000000000000000000000000000
χ45222222222-22222-2-2-2-2-2-22-2-2-22-22-2-2222-22-2200000000000000000000-22-220000000000002200-2-200002-22-2000000000000000000
χ46222222222-22222-2-2-2-2-2-22-2-2-22-22-2-2222-22-2200000000000000000000-22-22000000000000-2-200220000-22-22000000000000000000
χ47222222222-22222-2-2-2-2-2-22-2-2-2-22-22-222-22-222000000000000000000002-22-20000000000002200-2-20000-22-22000000000000000000
χ48222222222-22222-2-2-2-2-2-22-2-2-2-22-22-222-22-222000000000000000000002-22-2000000000000-2-2002200002-22-2000000000000000000
χ49222222222-2-2-2-2-2-22222-22-22-2000022-20000-2002200222-22-2-22-22000000000000-2-2-2-2000000000000000000000000002-22-2000000
χ50222222222-2-2-2-2-2-22222-22-22-2000022-20000-200220022-22-222-22-2000000000000-2-2-2-200000000000000000000000000-22-22000000
χ51222222222-2-2-2-2-2-22222-22-22-2000022-20000-200-2-200-2-22-22-2-22-22000000000000222200000000000000000000000000-22-22000000
χ52222222222-2-2-2-2-2-22222-22-22-2000022-20000-200-2-200-2-2-22-222-22-20000000000002222000000000000000000000000002-22-2000000
χ532222-2-2-2-22222-2-22-2-222-2-2-2-222-2-2222-22-2-222000000000000000000002-2-22000000002-2-220000002-2-220000000000000000000000
χ542222-2-2-2-22222-2-22-2-222-2-2-2-222-2-2222-22-2-222000000000000000000002-2-2200000000-222-2000000-222-20000000000000000000000
χ552222-2-2-2-22222-2-22-2-222-2-2-2-22-222-222-2-222-2200000000000000000000-222-2000000002-2-22000000-222-20000000000000000000000
χ562222-2-2-2-22222-2-22-2-222-2-2-2-22-222-222-2-222-2200000000000000000000-222-200000000-222-20000002-2-220000000000000000000000
χ572222-2-2-2-222-2-222222-2-2-2-2-2220000-2220000-22200-2-2002i−2i−2i2i2i−2i−2i2i00000000-2-222000000000000000000000000002i−2i−2i2i0000000000
χ582222-2-2-2-222-2-222222-2-2-2-2-2220000-2220000-22200-2-200−2i2i2i−2i−2i2i2i−2i00000000-2-22200000000000000000000000000−2i2i2i−2i0000000000
χ592222-2-2-2-222-2-222222-2-2-2-2-2220000-2220000-2-2-20022002i−2i−2i2i2i−2i−2i2i0000000022-2-200000000000000000000000000−2i2i2i−2i0000000000
χ602222-2-2-2-222-2-222222-2-2-2-2-2220000-2220000-2-2-2002200−2i2i2i−2i−2i2i2i−2i0000000022-2-2000000000000000000000000002i−2i−2i2i0000000000
χ612222-2-2-2-22-222-2-2-222-2-22-222-222-2-2-22-222-2-22000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2-222000000000000002i−2i0000000000000000000000000000
χ622222-2-2-2-22-222-2-2-222-2-22-222-222-2-2-22-222-2-2200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-22200000000000000−2i2i0000000000000000000000000000
χ632222-2-2-2-22-222-2-2-222-2-22-222-2-2-222-22-2-2-2222000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i22-2-200000000000000−2i2i0000000000000000000000000000
χ642222-2-2-2-22-222-2-2-222-2-22-222-2-2-222-22-2-2-222200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i22-2-2000000000000002i−2i0000000000000000000000000000
χ652222-2-2-2-22-222-2-2-2-2-222-222222-2-22-2-222-2-22-200000000000000000000-222-20000000000002i−2i00−2i2i00002i−2i−2i2i000000000000000000
χ662222-2-2-2-22-222-2-2-2-2-222-222222-2-22-2-222-2-22-200000000000000000000-222-2000000000000−2i2i002i−2i0000−2i2i2i−2i000000000000000000
χ672222-2-2-2-22-222-2-2-2-2-222-22222-222-2-2-22-222-2-2000000000000000000002-2-220000000000002i−2i00−2i2i0000−2i2i2i−2i000000000000000000
χ682222-2-2-2-22-222-2-2-2-2-222-22222-222-2-2-22-222-2-2000000000000000000002-2-22000000000000−2i2i002i−2i00002i−2i−2i2i000000000000000000
χ692222-2-2-2-22-2-2-222-222-2-2-222-2200002-2-200002002-2002-22i−2i−2i2i−2i2i2i−2i000000000000-2-222000000000000000000000000002i−2i−2i2i000000
χ702222-2-2-2-22-2-2-222-222-2-2-222-2200002-2-200002002-2002-2−2i2i2i−2i2i−2i−2i2i000000000000-2-22200000000000000000000000000−2i2i2i−2i000000
χ712222-2-2-2-22-2-2-222-222-2-2-222-2200002-2-20000200-2200-222i−2i−2i2i−2i2i2i−2i00000000000022-2-200000000000000000000000000−2i2i2i−2i000000
χ722222-2-2-2-22-2-2-222-222-2-2-222-2200002-2-20000200-2200-22−2i2i2i−2i2i−2i−2i2i00000000000022-2-2000000000000000000000000002i−2i−2i2i000000
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χ8044-4-44-44-4404-44-400000000000-40-400004040-222-2-22-220000000000000000-22-222-22-2000000000000000000000000000000000000
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χ8744-4-4-44-44404-4-4400000000000-404000040-402-2-2-2-222200000000000000002-2-22-222-2000000000000000000000000000000000000
χ8844-4-4-44-44404-4-4400000000000-404000040-40-22222-2-2-20000000000000000-222-22-2-22000000000000000000000000000000000000
χ8944-4-4-44-4440-444-4000000000040-40000-404002-2-2-2-22220000000000000000-222-22-2-22000000000000000000000000000000000000
χ9044-4-4-44-4440-444-4000000000040-40000-40400-22222-2-2-200000000000000002-2-22-222-2000000000000000000000000000000000000
χ9144-4-4-44-4440-444-40000000000-404000040-4002-222-22-2-20000000000000000-222-2-222-2000000000000000000000000000000000000
χ9244-4-4-44-4440-444-40000000000-404000040-400-22-2-22-22200000000000000002-2-222-2-22000000000000000000000000000000000000
χ93888-888-8-8-800000000000000000000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ94888-888-8-8-80000000000000000000000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ95888-8-8-888-800000000000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ96888-8-8-888-80000000000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ9788-888-8-88-80000008-88-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-888-8-88-8000000-88-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-88-888-8-80000008-8-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-88-888-8-8000000-888-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10116-16000000080000-800000000000000000000000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ10216-16000000080000-80000000000000000000000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ10316-160000000-800008000000000000000000000000000000000000000000000000000000000000000000000004-40000000000000000
χ10416-160000000-80000800000000000000000000000000000000000000000000000000000000000000000000000-440000000000000000

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