Finite Group Databasebeta

← Group #72319889

Character table — Group #72319889

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size1122222222222222222444444488888888888888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order1222222224444444488888888844444444888888881616161616161616161616161616161622224444444444888888161616161616161622444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-111-1-111
χ911111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1011111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1211111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ1311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-111-1-1
χ1511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ1611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ17111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−iii−i−ii−iii−i−i11-1-111-1-11-1i−i1-1i−i
χ18111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11i−i−i−iiii−i−i−iii11-1-111-1-1-11−ii-11−ii
χ19111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-11i−iii−i−ii−i−i−iii-1-111-1-1111-1i−i-11−ii
χ20111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1-111-1i−i−i−iiii−iii−i−i-1-111-1-111-11−ii1-1i−i
χ21111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-111-1-11−ii−i−iii−iiii−i−i-1-111-1-1111-1−ii-11i−i
χ22111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i-111-1-111-1−iiii−i−i−ii−i−iii-1-111-1-111-11i−i1-1−ii
χ23111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−i−iii−ii−i−iii11-1-111-1-11-1−ii1-1−ii
χ24111-11-11-1-111-1-111-1-1-1-111-1-111-111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11−iiii−i−i−iiii−i−i11-1-111-1-1-11i−i-11i−i
χ25111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11−iiii−i−i−ii−i−iii11-1-1-1-111-11−ii1-1i−i
χ26111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−ii−i−iii−iiii−i−i11-1-1-1-1111-1i−i-11−ii
χ27111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-11-11-1−iiii−i−i−iiii−i−i-1-11111-1-1-11−ii-11−ii
χ28111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-11-11−ii−i−iii−ii−i−iii-1-11111-1-11-1i−i1-1i−i
χ29111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-11-11-11-1i−i−i−iiii−i−i−iii-1-11111-1-1-11i−i-11i−i
χ30111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-11-11-11i−iii−i−ii−iii−i−i-1-11111-1-11-1−ii1-1−ii
χ31111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111−i−iii-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11i−i−i−iiii−iii−i−i11-1-1-1-111-11i−i1-1−ii
χ32111-11-11-1-111-1-111-1-1-1-111-1-111-1-1-111−i−iii-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−iii−i−ii−i−i−iii11-1-1-1-1111-1−ii-11i−i
χ3322222222222222222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000220000-2-200000000000000000000
χ3422222222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000-2-200002200000000000000000000
χ3522222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-200002200000000000000000000
χ3622222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000220000-2-200000000000000000000
χ372222-2-2-22-22-2222-2-2-222-2-22-222-20000000000000000000000002i2i−2i−2i2i2i−2i−2i002200-2-2002i−2i2i−2i0000000000000000000000
χ382222-2-2-22-22-2222-2-2-222-2-22-222-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00-2-2002200−2i2i−2i2i0000000000000000000000
χ392222-2-2-22-22-2222-2-2-222-2-22-222-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i002200-2-200−2i2i−2i2i0000000000000000000000
χ402222-2-2-22-22-2222-2-2-222-2-22-222-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00-2-20022002i−2i2i−2i0000000000000000000000
χ41222-22-22-2-222-2-222-2-222-2-222-2-2222-2-22i2i−2i−2i-2-222−2i−2i2i2i0000000000000000000000002i−2i0000−2i2i00000000000000000000
χ42222-22-22-2-222-2-222-2-222-2-222-2-2222-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000−2i2i00002i−2i00000000000000000000
χ43222-22-22-2-222-2-222-2-222-2-222-2-22-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000−2i2i00002i−2i00000000000000000000
χ44222-22-22-2-222-2-222-2-222-2-222-2-22-2-222−2i−2i2i2i22-2-22i2i−2i−2i0000000000000000000000002i−2i0000−2i2i00000000000000000000
χ45222-2-22-2-222-2-2-22-222-2-2-2-2-2222200000000000000000000000022-2-2-2-222002-200-22002-2-220000000000000000000000
χ46222-2-22-2-222-2-2-22-222-2-2-2-2-2222200000000000000000000000022-2-2-2-22200-22002-200-222-20000000000000000000000
χ47222-2-22-2-222-2-2-22-222-2-2-2-2-22222000000000000000000000000-2-22222-2-2002-200-2200-222-20000000000000000000000
χ48222-2-22-2-222-2-2-22-222-2-2-2-2-22222000000000000000000000000-2-22222-2-200-22002-2002-2-220000000000000000000000
χ4922-222-2-2-22-2-22-222-22222-2-2-22-220000000000000000000000002-22-22-22-22200-2-200000000002-22-20000000000000000
χ5022-222-2-2-22-2-22-222-22222-2-2-22-220000000000000000000000002-22-22-22-2-2-200220000000000-22-220000000000000000
χ5122-222-2-2-22-2-22-222-22222-2-2-22-22000000000000000000000000-22-22-22-222200-2-20000000000-22-220000000000000000
χ5222-222-2-2-22-2-22-222-22222-2-2-22-22000000000000000000000000-22-22-22-22-2-2002200000000002-22-20000000000000000
χ5322-22-222-2-2-222-22-22-222-22-222-2-200002i−2i2i−2i00002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000002-22-200000000
χ5422-22-222-2-2-222-22-22-222-22-222-2-200002i−2i2i−2i00002i−2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000-22-2200000000
χ5522-22-222-2-2-222-22-22-222-22-222-2-20000−2i2i−2i2i0000−2i2i−2i2i000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000-22-2200000000
χ5622-22-222-2-2-222-22-22-222-22-222-2-20000−2i2i−2i2i0000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000002-22-200000000
χ5722-22-222-2-2-222-22-22-2-2-22-22-2-22200002i−2i2i−2i0000−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22-2000000000000
χ5822-22-222-2-2-222-22-22-2-2-22-22-2-22200002i−2i2i−2i0000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22-22000000000000
χ5922-22-222-2-2-222-22-22-2-2-22-22-2-2220000−2i2i−2i2i00002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22-22000000000000
χ6022-22-222-2-2-222-22-22-2-2-22-22-2-2220000−2i2i−2i2i00002i−2i2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-22-2000000000000
χ6122-2-222-22-2-2-2-22222-2-2-22-2222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i2-200-2200000000002i−2i−2i2i0000000000000000
χ6222-2-222-22-2-2-2-22222-2-2-22-2222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i-22002-20000000000−2i2i2i−2i0000000000000000
χ6322-2-222-22-2-2-2-22222-2-2-22-2222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i2-200-220000000000−2i2i2i−2i0000000000000000
χ6422-2-222-22-2-2-2-22222-2-2-22-2222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i-22002-200000000002i−2i−2i2i0000000000000000
χ6522-2-2-2-2222-22-222-2-22222-2-22-22-200002-2-220000-222-222-2-2-2-22200000000000000000000000000002-2-22000000000000
χ6622-2-2-2-2222-22-222-2-22222-2-22-22-200002-2-220000-222-2-2-22222-2-20000000000000000000000000000-222-2000000000000
χ6722-2-2-2-2222-22-222-2-22222-2-22-22-20000-222-200002-2-2222-2-2-2-2220000000000000000000000000000-222-2000000000000
χ6822-2-2-2-2222-22-222-2-22222-2-22-22-20000-222-200002-2-22-2-22222-2-200000000000000000000000000002-2-22000000000000
χ6922-2-2-2-2222-22-222-2-22-2-2-222-22-2200002-2-2200002-2-22000000002-2-22-222-20000000000000000000000002-2-2200000000
χ7022-2-2-2-2222-22-222-2-22-2-2-222-22-2200002-2-2200002-2-2200000000-222-22-2-22000000000000000000000000-222-200000000
χ7122-2-2-2-2222-22-222-2-22-2-2-222-22-220000-222-20000-222-2000000002-2-22-222-2000000000000000000000000-222-200000000
χ7222-2-2-2-2222-22-222-2-22-2-2-222-22-220000-222-20000-222-200000000-222-22-2-220000000000000000000000002-2-2200000000
χ73444444444-4-4-4-4-4-4-4-40000000004-44-40000000000000000000000000000000000000000000000000000000000000000
χ74444444444-4-4-4-4-4-4-4-4000000000-44-440000000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-44-44-4444-4-4-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-44-4-44-4-4-4444000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ774444-4-4-44-4-44-4-4-44440000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ78444-44-44-4-4-4-444-4-4440000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ79444-44-44-4-4-4-444-4-444000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ80444-4-44-4-444-4-4-44-44444444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ81444-4-44-4-44-4444-44-4-400000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ82444-4-44-4-44-4444-44-4-40000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ8344-444-4-4-4444-44-4-44-400000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ8444-444-4-4-4444-44-4-44-40000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ8544-444-4-4-44-4-44-444-44-4-4-4444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ8644-44-444-4-44-4-44-44-44000000000000000004-44-400000000000000000000000000000000000000000000000000000000
χ8744-44-444-4-44-4-44-44-4400000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ8844-4-444-44-4444-4-4-4-44000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ8944-4-444-44-4444-4-4-4-440000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ9044-4-444-44-4-4-4-44444-444-44-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-4-4-44444-44-4-444-4000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-44444-44-4-444-400000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ9316-1600000000000000082−82000000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-16000000000000000−8282000000000000000000000000000000000000000000000000000000000000000000000000000

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