Finite Group Databasebeta

← Group #72309777

Character table — Group #72309777

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111222222222222444444444444444444444444444888888888888888888888888888161616161616161616161616161616161616323232323232323232323232
order12222244444488882244444888888888888161616161616161622244488888888816161616161616161616161644448888881616161616161616444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111-1-1111-1-1-1-111-1-1-1-111111111111-1-111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ6111111111111111111-1-1111-1-1-1-111-1-1-1-111111111111-1-111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ7111111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ8111111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-11111-1-1-1-11111-1-11111-1-111-1-1
χ91111111111111111-1-111111-1-1-1-111-1-1-1-11111111111-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ101111111111111111-1-111111-1-1-1-111-1-1-1-11111111111-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ111111111111111111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ171111-1-11111-1-1111111111-1-11111-1-11111111111-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-11111-1-1-1-1ii−i−i-1-1ii−i−i11-1-111-1-1i−ii−ii−ii−ii−ii−i
χ181111-1-11111-1-1111111111-1-11111-1-11111111111-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-11111-1-1-1-1−i−iii-1-1−i−iii11-1-111-1-1−ii−ii−ii−ii−ii−ii
χ191111-1-11111-1-1111111111-1-11111-1-1111111-1-1-1-11111-11-11-1-1-1-1-11111-1-1-1-111-1-1-1-11111ii−i−i-1-1−i−iii-1-111-1-111i−ii−i−ii−iii−i−ii
χ201111-1-11111-1-1111111111-1-11111-1-1111111-1-1-1-11111-11-11-1-1-1-1-11111-1-1-1-111-1-1-1-11111−i−iii-1-1ii−i−i-1-111-1-111−ii−iii−ii−i−iii−i
χ211111-1-11111-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-11111-1-11111-1-1-1-1-1-11111ii−i−i-11ii−i−i11-1-1-1-111i−i−iii−i−ii−ii−ii
χ221111-1-11111-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-11111-1-11111-1-1-1-1-1-11111−i−iii-11−i−iii11-1-1-1-111−iii−i−iii−ii−ii−i
χ231111-1-11111-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-11111-1-111-1-1111111-1-1-1-1ii−i−i-11−i−iii-1-11111-1-1i−i−ii−iii−i−iii−i
χ241111-1-11111-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-11111-1-111-1-1111111-1-1-1-1−i−iii-11ii−i−i-1-11111-1-1−iii−ii−i−iii−i−ii
χ251111-1-11111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-111-1-1111111-1-1-1-1-1-11111ii−i−i1-1ii−i−i-1-11111-1-1−iii−i−iii−i−ii−ii
χ261111-1-11111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-111-1-1111111-1-1-1-1-1-11111−i−iii1-1−i−iii-1-11111-1-1i−i−iii−i−iii−ii−i
χ271111-1-11111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111-1-11111-1-1111111-1-1-1-1ii−i−i1-1−i−iii11-1-1-1-111−iii−ii−i−ii−iii−i
χ281111-1-11111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111-1-11111-1-1111111-1-1-1-1−i−iii1-1ii−i−i11-1-1-1-111i−i−ii−iii−ii−i−ii
χ291111-1-11111-1-11111-1-1-1-11-1-11111-1-11111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−i11ii−i−i-1-111-1-111−ii−ii−ii−iii−ii−i
χ301111-1-11111-1-11111-1-1-1-11-1-11111-1-11111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii11−i−iii-1-111-1-111i−ii−ii−ii−i−ii−ii
χ311111-1-11111-1-11111-1-1-1-11-1-11111-1-1111111-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i11−i−iii11-1-111-1-1−ii−iii−ii−ii−i−ii
χ321111-1-11111-1-11111-1-1-1-11-1-11111-1-1111111-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii11ii−i−i11-1-111-1-1i−ii−i−ii−ii−iii−i
χ33222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-200000000222222-222-2-2-2-2-2-20000000000000000-2-2000000000000000000000000
χ34222222222222-2-2-2-222-2-2222-2-2-2-2-2-22222-2-2000000002-2-222-2-2-2-2-2-222220000000000000000-22000000000000000000000000
χ35222222222222-2-2-2-2-2-222222-2-2-2-2-2-22222-2-200000000-222-2-22-2-2-222-2-22200000000000000002-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2222222-2-2000000000000000022000000000000000000000000
χ3722222222-2-2-2-200002222-22-222-2-200000000i2i2−i2−i2i2i2−i2−i22-2-2-2-2202-2000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ3822222222-2-2-2-200002222-22-222-2-200000000−i2−i2i2i2−i2−i2i2i22-2-2-2-2202-2000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ3922222222-2-2-2-2000022-2-2-22-2-2-22200000000i2i2−i2−i2i2i2−i2−i2222-2-2-20-22000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4022222222-2-2-2-2000022-2-2-22-2-2-22200000000−i2−i2i2i2−i2−i2i2i2222-2-2-20-22000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4122222222-2-2-2-20000-2-222-22-2-2-22200000000i2i2−i2−i2i2i2−i2−i2-2-2-22220-22000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4222222222-2-2-2-20000-2-222-22-2-2-22200000000−i2−i2i2i2−i2−i2i2i2-2-2-22220-22000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4322222222-2-2-2-20000-2-2-2-2-22-222-2-200000000i2i2−i2−i2i2i2−i2−i2-22222-202-2000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4422222222-2-2-2-20000-2-2-2-2-22-222-2-200000000−i2−i2i2i2−i2−i2i2i2-22222-202-2000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ45222222-2-2222222220000-2-2-20000220000-2-222222222000000-200000000-2-2-2-2000000002-22-2002-22-200000000000000000000
χ46222222-2-2222222220000-2-2-20000220000-2-222222222000000-200000000-2-2-2-200000000-22-2200-22-2200000000000000000000
χ47222222-2-2222222220000-2-2-20000220000-2-2-2-2-2-2-2-2-2-2000000-2000000002222000000002-22-200-22-2200000000000000000000
χ48222222-2-2222222220000-2-2-20000220000-2-2-2-2-2-2-2-2-2-2000000-200000000222200000000-22-22002-22-200000000000000000000
χ492222-2-22222-2-2-2-2-2-222222-2-2222222-2-2-2-2-2-200000000-22-22-2-22-2-2-2-2-2-222000000000000000022000000000000000000000000
χ502222-2-22222-2-2-2-2-2-222-2-22-2-2-2-2-2-2222222-2-200000000-2-222-22222-2-222-2-200000000000000002-2000000000000000000000000
χ512222-2-22222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2222222-2-20000000022-2-22-222222-2-2-2-20000000000000000-22000000000000000000000000
χ522222-2-22222-2-2-2-2-2-2-2-2-2-22-2-2222222-2-2-2-2-2-2000000002-22-2222-2-22222220000000000000000-2-2000000000000000000000000
χ532222-2-222-2-22200002222-2-2222-2-200000000i2i2−i2−i2−i2−i2i2i2-2-22-22-20-22000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ542222-2-222-2-22200002222-2-2222-2-200000000−i2−i2i2i2i2i2−i2−i2-2-22-22-20-22000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ552222-2-222-2-222000022-2-2-2-22-2-22200000000i2i2−i2−i2−i2−i2i2i2-22-2-22202-2000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ562222-2-222-2-222000022-2-2-2-22-2-22200000000−i2−i2i2i2i2i2−i2−i2-22-2-22202-2000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ572222-2-222-2-2220000-2-222-2-22-2-22200000000i2i2−i2−i2−i2−i2i2i22-222-2-202-2000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ582222-2-222-2-2220000-2-222-2-22-2-22200000000−i2−i2i2i2i2i2−i2−i22-222-2-202-2000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2−i2i2i2−i2000000000000
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χ602222-2-222-2-2220000-2-2-2-2-2-2222-2-200000000−i2−i2i2i2i2i2−i2−i222-22-220-22000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ612222-2-2-2-222-2-222220000-2220000-2-20000-2-22222-2-2-2-2000000200000000-2-222000000002i−2i−2i2i002i−2i−2i2i00000000000000000000
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χ642222-2-2-2-222-2-222220000-2220000-2-20000-2-2-2-2-2-2222200000020000000022-2-200000000−2i2i2i−2i002i−2i−2i2i00000000000000000000
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χ9588-8-800-8800004i2−4i24i2−4i200000000000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000
χ9688-8-800-880000−4i24i2−4i24i2000000000000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8000000004i2−4i2−4i24i200000000042−42004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8000000004i2−4i2−4i24i2000000000−424200−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800000000−4i24i24i2−4i200000000042−4200−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-800000000−4i24i24i2−4i2000000000−4242004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000

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