Finite Group Databasebeta

← Group #72319692

Character table — Group #72319692

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size111122222244444444444444448888888888888888888888888888888888888888888888888888881616161616161616323232323232323232323232
order1222222222222222224444444422222222444444444444444444444444444444444444444444444422444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ171-1-1111-1-11-111-1-111-1-11-1ii−i−i1-111-1-11-11-1ii−i−iii−i−iii−i−i1-11-111-1-111-1-111-1-1iii−i−i−iii−i−iii−i−iii−i−i1-11-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-1-1111-1-11-111-1-111-1-11-1ii−i−i1-111-1-11-11-1ii−i−iii−i−iii−i−i1-11-111-1-111-1-111-1-1iii−i−i−iii−i−iii−i−iii−i−i-11-11−i−iii-11−ii-11−ii-11−ii
χ191-1-1111-1-11-111-1-111-1-11-1ii−i−i1-111-1-1-11-11ii−i−i−i−iii−i−iii-11-1111-1-1-1-111-1-111iii−i−i−iii−i−i−i−iii−i−iii1-11-1ii−i−i-11−ii-11−ii1-1i−i
χ201-1-1111-1-11-111-1-111-1-11-1ii−i−i1-111-1-1-11-11ii−i−i−i−iii−i−iii-11-1111-1-1-1-111-1-111iii−i−i−iii−i−i−i−iii−i−iii-11-11−i−iii1-1i−i1-1i−i-11−ii
χ211-1-1111-1-11-111-1-111-1-11-1ii−i−i1-1-1-1111-1-11−i−iiiii−i−i−i−iii1-1-11-1-11111-1-1-1-111iii−i−i−i−i−iiiii−i−i−i−iii1-11-1ii−i−i1-1i−i-11−ii-11−ii
χ221-1-1111-1-11-111-1-111-1-11-1ii−i−i1-1-1-1111-1-11−i−iiiii−i−i−i−iii1-1-11-1-11111-1-1-1-111iii−i−i−i−i−iiiii−i−i−i−iii-11-11−i−iii-11−ii1-1i−i1-1i−i
χ231-1-1111-1-11-111-1-111-1-11-1ii−i−i1-1-1-111-111-1−i−iii−i−iiiii−i−i-111-1-1-111-1-11111-1-1iii−i−i−i−i−iii−i−iiiii−i−i1-11-1ii−i−i-11−ii1-1i−i-11−ii
χ241-1-1111-1-11-111-1-111-1-11-1ii−i−i1-1-1-111-111-1−i−iii−i−iiiii−i−i-111-1-1-111-1-11111-1-1iii−i−i−i−i−iii−i−iiiii−i−i-11-11−i−iii1-1i−i-11−ii1-1i−i
χ251-1-1111-1-11-111-1-111-1-11-1−i−iii1-111-1-11-11-1−i−iii−i−iii−i−iii1-11-111-1-111-1-111-1-1−i−i−iiii−i−iii−i−iii−i−iii1-11-1−i−iii1-1−ii1-1−ii1-1−ii
χ261-1-1111-1-11-111-1-111-1-11-1−i−iii1-111-1-11-11-1−i−iii−i−iii−i−iii1-11-111-1-111-1-111-1-1−i−i−iiii−i−iii−i−iii−i−iii-11-11ii−i−i-11i−i-11i−i-11i−i
χ271-1-1111-1-11-111-1-111-1-11-1−i−iii1-111-1-1-11-11−i−iiiii−i−iii−i−i-11-1111-1-1-1-111-1-111−i−i−iiii−i−iiiii−i−iii−i−i1-11-1−i−iii-11i−i-11i−i1-1−ii
χ281-1-1111-1-11-111-1-111-1-11-1−i−iii1-111-1-1-11-11−i−iiiii−i−iii−i−i-11-1111-1-1-1-111-1-111−i−i−iiii−i−iiiii−i−iii−i−i-11-11ii−i−i1-1−ii1-1−ii-11i−i
χ291-1-1111-1-11-111-1-111-1-11-1−i−iii1-1-1-1111-1-11ii−i−i−i−iiiii−i−i1-1-11-1-11111-1-1-1-111−i−i−iiiiii−i−i−i−iiiii−i−i1-11-1−i−iii1-1−ii-11i−i-11i−i
χ301-1-1111-1-11-111-1-111-1-11-1−i−iii1-1-1-1111-1-11ii−i−i−i−iiiii−i−i1-1-11-1-11111-1-1-1-111−i−i−iiiiii−i−i−i−iiiii−i−i-11-11ii−i−i-11i−i1-1−ii1-1−ii
χ311-1-1111-1-11-111-1-111-1-11-1−i−iii1-1-1-111-111-1ii−i−iii−i−i−i−iii-111-1-1-111-1-11111-1-1−i−i−iiiiii−i−iii−i−i−i−iii1-11-1−i−iii-11i−i1-1−ii-11i−i
χ321-1-1111-1-11-111-1-111-1-11-1−i−iii1-1-1-111-111-1ii−i−iii−i−i−i−iii-111-1-1-111-1-11111-1-1−i−i−iiiiii−i−iii−i−i−i−iii-11-11ii−i−i1-1−ii-11i−i1-1−ii
χ3322222222222-22-22-22-2-2-22222-2-20000002200000000-2-2-2-2002200000000-2-2-2-22-2-22-2-200000000222200000000000000000000
χ3422222222222-22-22-22-2-2-22222-2-2000000-2-200000000222200-2-20000000022222-2-22-2-200000000-2-2-2-200000000000000000000
χ3522222222222-22-22-22-2-2-2-2-2-2-2-2-200000022000000002222002200000000-2-2-2-2-222-22200000000-2-2-2-200000000000000000000
χ3622222222222-22-22-22-2-2-2-2-2-2-2-2-2000000-2-200000000-2-2-2-200-2-2000000002222-222-22200000000222200000000000000000000
χ372222222222-22-22-22-22-2-22222-2-2000022000000-2-2-2-2000022000000-2-2-2-20000-22-2-22-200002222000000000000000000000000
χ382222222222-22-22-22-22-2-22222-2-20000-2-200000022220000-2-200000022220000-22-2-22-20000-2-2-2-2000000000000000000000000
χ392222222222-22-22-22-22-2-2-2-2-2-2-2-20000220000002222000022000000-2-2-2-200002-222-220000-2-2-2-2000000000000000000000000
χ402222222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-2000000-2-2-2-20000-2-2000000222200002-222-2200002222000000000000000000000000
χ412222222222-2-2-2-2-2-2-2-22222222222220000-2-2-2-2000000000000-2-2-2-200000000-2-22-2-2222220000000000000000000000000000
χ422222222222-2-2-2-2-2-2-2-222222222-2-2-2-200002222000000000000222200000000-2-22-2-22-2-2-2-20000000000000000000000000000
χ432222222222-2-2-2-2-2-2-2-222-2-2-2-222222200002222000000000000-2-2-2-20000000022-222-2-2-2-2-20000000000000000000000000000
χ442222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-20000-2-2-2-200000000000022220000000022-222-222220000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-222-2200002-22-22-2000000002-22-22-22-200002-22-20000000000000000002-22-22-22-200000000000000000000
χ462222-2-2-2-22222-2-2-2-222-2200002-22-22-200000000-22-22-22-2200002-22-2000000000000000000-22-22-22-2200000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2200002-2-22-22000000002-22-2-22-220000-22-220000000000000000002-22-2-22-2200000000000000000000
χ482222-2-2-2-22222-2-2-2-222-2200002-2-22-2200000000-22-222-22-20000-22-22000000000000000000-22-222-22-200000000000000000000
χ492222-2-2-2-2222-2-22-222-22-20000-22000022002-22-200002-22-2-2-20000002-22-200000000002-22-20000-22-2200000000000000000000
χ502222-2-2-2-2222-2-22-222-22-20000-2200002200-22-220000-22-22-2-20000002-22-20000000000-22-2200002-22-200000000000000000000
χ512222-2-2-2-2222-2-22-222-22-20000-220000-2-2002-22-20000-22-2222000000-22-2200000000002-22-200002-22-200000000000000000000
χ522222-2-2-2-2222-2-22-222-22-20000-220000-2-200-22-2200002-22-222000000-22-220000000000-22-220000-22-2200000000000000000000
χ532222-2-2-2-222-222-22-2-222-20000-22000000222-22-22-22-2000000-2-2000000002-22-2000000-22-22-22-22000000000000000000000000
χ542222-2-2-2-222-222-22-2-222-20000-2200000022-22-22-22-22000000-2-2000000002-22-20000002-22-22-22-2000000000000000000000000
χ552222-2-2-2-222-222-22-2-222-20000-22000000-2-22-22-2-22-220000002200000000-22-22000000-22-222-22-2000000000000000000000000
χ562222-2-2-2-222-222-22-2-222-20000-22000000-2-2-22-222-22-20000002200000000-22-220000002-22-2-22-22000000000000000000000000
χ572222-2-2-2-222-2-22222-2-2-2200002-22-22-222-2-2000000000000-2-222-22-22-22-222-22-200000000000000000000000000000000000000
χ582222-2-2-2-222-2-22222-2-2-2200002-22-22-2-2-22200000000000022-2-2-22-222-22-2-22-2200000000000000000000000000000000000000
χ592222-2-2-2-222-2-22222-2-2-2200002-2-22-222222000000000000-2-2-2-22-22-2-22-22-22-2200000000000000000000000000000000000000
χ602222-2-2-2-222-2-22222-2-2-2200002-2-22-22-2-2-2-200000000000022222-22-22-22-22-22-200000000000000000000000000000000000000
χ612-2-2222-2-22-22-2-222-2-22-222i2i−2i−2i-220000002-200000000−2i−2i2i2i002-200000000-2-2222i−2i−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ622-2-2222-2-22-22-2-222-2-22-222i2i−2i−2i-22000000-22000000002i2i−2i−2i00-220000000022-2-22i−2i−2i−2i2i2i00000000−2i−2i2i2i00000000000000000000
χ632-2-2222-2-22-22-2-222-2-22-22−2i−2i2i2i-220000002-2000000002i2i−2i−2i002-200000000-2-222−2i2i2i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ642-2-2222-2-22-22-2-222-2-22-22−2i−2i2i2i-22000000-2200000000−2i−2i2i2i00-220000000022-2-2−2i2i2i2i−2i−2i000000002i2i−2i−2i00000000000000000000
χ652-2-2222-2-22-2-222-2-222-2-222i2i−2i−2i-2200002-2000000−2i−2i2i2i00002-2000000-2-2220000−2i2i−2i2i−2i2i00002i2i−2i−2i000000000000000000000000
χ662-2-2222-2-22-2-222-2-222-2-222i2i−2i−2i-220000-220000002i2i−2i−2i0000-2200000022-2-20000−2i2i−2i2i−2i2i0000−2i−2i2i2i000000000000000000000000
χ672-2-2222-2-22-2-222-2-222-2-22−2i−2i2i2i-2200002-20000002i2i−2i−2i00002-2000000-2-22200002i−2i2i−2i2i−2i0000−2i−2i2i2i000000000000000000000000
χ682-2-2222-2-22-2-222-2-222-2-22−2i−2i2i2i-220000-22000000−2i−2i2i2i0000-2200000022-2-200002i−2i2i−2i2i−2i00002i2i−2i−2i000000000000000000000000
χ692-2-2222-2-22-2-2-222-2-2222-22i2i−2i−2i2-222-2-20000−2i−2i2i2i000000000000-2-22200000000−2i−2i2i2i2i−2i2i2i−2i−2i0000000000000000000000000000
χ702-2-2222-2-22-2-2-222-2-2222-22i2i−2i−2i2-2-2-22200002i2i−2i−2i00000000000022-2-200000000−2i−2i2i2i2i−2i−2i−2i2i2i0000000000000000000000000000
χ712-2-2222-2-22-2-2-222-2-2222-2−2i−2i2i2i2-222-2-200002i2i−2i−2i000000000000-2-222000000002i2i−2i−2i−2i2i−2i−2i2i2i0000000000000000000000000000
χ722-2-2222-2-22-2-2-222-2-2222-2−2i−2i2i2i2-2-2-2220000−2i−2i2i2i00000000000022-2-2000000002i2i−2i−2i−2i2i2i2i−2i−2i0000000000000000000000000000
χ732-2-22-2-2222-22222-2-2-2-2-2-20000222-2-22000000002i−2i−2i2i2i−2i−2i2i00002-2-220000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ742-2-22-2-2222-22222-2-2-2-2-2-20000222-2-2200000000−2i2i2i−2i−2i2i2i−2i00002-2-22000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ752-2-22-2-2222-22222-2-2-2-2-2-2000022-222-2000000002i−2i−2i2i−2i2i2i−2i0000-222-20000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ762-2-22-2-2222-22222-2-2-2-2-2-2000022-222-200000000−2i2i2i−2i2i−2i−2i2i0000-222-2000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ772-2-22-2-2222-22-22-2-22-22220000-2-200002-2002i−2i−2i2i00002i−2i−2i2i-220000002-2-2200000000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ782-2-22-2-2222-22-22-2-22-22220000-2-200002-200−2i2i2i−2i0000−2i2i2i−2i-220000002-2-220000000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ792-2-22-2-2222-22-22-2-22-22220000-2-20000-22002i−2i−2i2i0000−2i2i2i−2i2-2000000-222-200000000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ802-2-22-2-2222-22-22-2-22-22220000-2-20000-2200−2i2i2i−2i00002i−2i−2i2i2-2000000-222-20000000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ812-2-22-2-2222-2-22-222-22-2220000-2-20000002-22i−2i−2i2i2i−2i−2i2i000000-22000000002-2-22000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ822-2-22-2-2222-2-22-222-22-2220000-2-20000002-2−2i2i2i−2i−2i2i2i−2i000000-22000000002-2-220000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ832-2-22-2-2222-2-22-222-22-2220000-2-2000000-222i−2i−2i2i−2i2i2i−2i0000002-200000000-222-2000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ842-2-22-2-2222-2-22-222-22-2220000-2-2000000-22−2i2i2i−2i2i−2i−2i2i0000002-200000000-222-20000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ852-2-22-2-2222-2-2-2-2-22222-2-20000222-2-222-2-22000000000000-222-2-222-2-222-22-2-2200000000000000000000000000000000000000
χ862-2-22-2-2222-2-2-2-2-22222-2-20000222-2-22-222-20000000000002-2-22-222-22-2-22-222-200000000000000000000000000000000000000
χ872-2-22-2-2222-2-2-2-2-22222-2-2000022-222-22-22-2000000000000-22-222-2-22-222-2-222-200000000000000000000000000000000000000
χ882-2-22-2-2222-2-2-2-2-22222-2-2000022-222-2-22-220000000000002-22-22-2-222-2-222-2-2200000000000000000000000000000000000000
χ8944444-44-4-4-400000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000000022-2-22i−2i2i−2i000000000000
χ9044444-44-4-4-400000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000-2-222−2i2i−2i2i000000000000
χ9144444-44-4-4-40000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000022-2-2−2i2i−2i2i000000000000
χ9244444-44-4-4-40000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000-2-2222i−2i2i−2i000000000000
χ934-4-444-4-44-4400000000004-4-44000000000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ944-4-444-4-44-4400000000004-4-4400000000000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ954-4-444-4-44-440000000000-444-4000000000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ964-4-444-4-44-440000000000-444-400000000000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ978888-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ991616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10016-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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