Finite Group Databasebeta

← Group #72310059

Character table — Group #72310059

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size111122222222222244444444444444444448888888888888888888888888881616161616161616161616161616161616161616323232323232323232323232
order122222444444888844488888888888888882244444488816161616161616161616161616161616444444448888888888882222888816161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1-1-111
χ171111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1ii−i−i111iiii−i−i−i−iiiii−i−i−i−i1-1i−ii−ii−i11-1-1i−ii−iii−i−i1-11-1i−ii−i1-11-1
χ181111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1ii−i−i111iiii−i−i−i−iiiii−i−i−i−i1-1i−i−ii−ii11-1-1−ii−iiii−i−i-11-11−ii−ii-11-11
χ191111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1−i−iii111−i−i−i−iiiii−i−i−i−iiiii1-1−iii−ii−i11-1-1i−ii−i−i−iii-11-11i−ii−i-11-11
χ201111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1−i−iii111−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii−ii11-1-1−ii−ii−i−iii1-11-1−ii−ii1-11-1
χ211111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-111ii−i−i111−i−i−i−iiiii−i−i−i−iiiii-11i−ii−ii−i-1-111i−ii−iii−i−i1-11-1−ii−ii-11-11
χ221111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-111ii−i−i111−i−i−i−iiiii−i−i−i−iiiii-11i−i−ii−ii-1-111−ii−iiii−i−i-11-11i−ii−i1-11-1
χ231111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-111−i−iii111iiii−i−i−i−iiiii−i−i−i−i-11−iii−ii−i-1-111i−ii−i−i−iii-11-11−ii−ii1-11-1
χ241111-1-1-11111-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-111−i−iii111iiii−i−i−i−iiiii−i−i−i−i-11−ii−ii−ii-1-111−ii−ii−i−iii1-11-1i−ii−i-11-11
χ251111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-1111-1-1ii−i−i1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1i−ii−i−ii-1-111i−i−ii−i−iii1-1-11i−i−ii1-1-11
χ261111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-1111-1-1ii−i−i1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1i−i−iii−i-1-111−iii−i−i−iii-111-1−iii−i-111-1
χ271111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-1111-1-1−i−iii1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i−ii-1-111i−i−iiii−i−i-111-1i−i−ii-111-1
χ281111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-1111-1-1−i−iii1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1−ii−iii−i-1-111−iii−iii−i−i1-1-11−iii−i1-1-11
χ291111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-11-1-111ii−i−i1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11i−ii−i−ii11-1-1i−i−ii−i−iii1-1-11−iii−i-111-1
χ301111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-11-1-111ii−i−i1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11i−i−iii−i11-1-1−iii−i−i−iii-111-1i−i−ii1-1-11
χ311111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-11-1-111−i−iii1-1-1iiii−i−i−i−i−i−i−i−iiiii-11−iii−i−ii11-1-1i−i−iiii−i−i-111-1−iii−i1-1-11
χ321111-1-1-11111-1-1-1-1-1-11-11-1-111111111-1-1-1-11-1-111−i−iii1-1-1iiii−i−i−i−i−i−i−i−iiiii-11−ii−iii−i11-1-1−iii−iii−i−i1-1-11i−i−ii-111-1
χ332222222222222222222-2222222-2-2-2-2-2-2-2-2-200000000-2-2-20000000000000000000022220000-2-2-2-20000000000000000
χ342222222222222222222-2222222-2-2-2-2-2-2-2-2-200000000-2-2-200000000000000000000-2-2-2-2000022220000000000000000
χ35222222222222-2-2-2-2222-2-2-2-2-2-2-22222-2-2-2-2-200000000-2220000000000000000000022-2-20000-2-2220000000000000000
χ36222222222222-2-2-2-2222-2-2-2-2-2-2-22222-2-2-2-2-200000000-22200000000000000000000-2-222000022-2-20000000000000000
χ37222222222-2-220000-2-2-22000000000022-2-2222222222-20022-2-222-2-200000000-2-2-2-20000000000000000000000000000
χ38222222222-2-220000-2-2-22000000000022-2-222222-2-2-2-2-200-2-222-2-22200000000-2-2220000000000000000000000000000
χ39222222222-2-220000-2-2-22000000000022-2-22-2-2-2-22222-200-2-222-2-2220000000022-2-20000000000000000000000000000
χ40222222222-2-220000-2-2-22000000000022-2-22-2-2-2-2-2-2-2-2-20022-2-222-2-20000000022220000000000000000000000000000
χ412222-2-2-22222-22222-22-2-222-2-2-2-222222222-200000000-2-2-2000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ422222-2-2-22222-22222-22-2-222-2-2-2-222222222-200000000-2-2-200000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ432222-2-2-22222-2-2-2-2-2-22-2-2-2-22222-2-2-2-22222-200000000-222000000000000000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ442222-2-2-22222-2-2-2-2-2-22-2-2-2-22222-2-2-2-22222-200000000-22200000000000000000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ452222-2-2-222-2-2-200002-2220000000000-2-222222-2-22i2i−2i−2i-2002i2i−2i−2i−2i−2i2i2i00000000-22−2i2i0000000000000000000000000000
χ462222-2-2-222-2-2-200002-2220000000000-2-222222-2-2−2i−2i2i2i-200−2i−2i2i2i2i2i−2i−2i00000000-222i−2i0000000000000000000000000000
χ472222-2-2-222-2-2-200002-2220000000000-2-2222-2-2222i2i−2i−2i-200−2i−2i2i2i2i2i−2i−2i000000002-2−2i2i0000000000000000000000000000
χ482222-2-2-222-2-2-200002-2220000000000-2-2222-2-222−2i−2i2i2i-2002i2i−2i−2i−2i−2i2i2i000000002-22i−2i0000000000000000000000000000
χ4922-2-22-222-200-222−2−2000-22−222−2−222−2−22-20022-22-22i−2i2i−2i02−22i−2i002i−2i00i2i2−i2−i2i2i2−i2−i2000000002−22−20000i2−i2i2−i2000000000000
χ5022-2-22-222-200-222−2−2000-22−222−2−222−2−22-20022-22-2−2i2i−2i2i02−2−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i2000000002−22−20000−i2i2−i2i2000000000000
χ5122-2-22-222-200-222−2−2000-22−222−2−222−2−22-2002-22-222i−2i2i−2i02−2−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i200000000−22−220000i2−i2i2−i2000000000000
χ5222-2-22-222-200-222−2−2000-22−222−2−222−2−22-2002-22-22−2i2i−2i2i02−22i−2i002i−2i00i2i2−i2−i2i2i2−i2−i200000000−22−220000−i2i2−i2i2000000000000
χ5322-2-22-222-200-2−2−222000-2−22−2−222−2−2222-20022-22-22i−2i2i−2i0−222i−2i002i−2i00−i2−i2i2i2−i2−i2i2i200000000−22−220000−i2i2−i2i2000000000000
χ5422-2-22-222-200-2−2−222000-2−22−2−222−2−2222-20022-22-2−2i2i−2i2i0−22−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i200000000−22−220000i2−i2i2−i2000000000000
χ5522-2-22-222-200-2−2−222000-2−22−2−222−2−2222-2002-22-222i−2i2i−2i0−22−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i2000000002−22−20000−i2i2−i2i2000000000000
χ5622-2-22-222-200-2−2−222000-2−22−2−222−2−2222-2002-22-22−2i2i−2i2i0−222i−2i002i−2i00−i2−i2i2i2−i2−i2i2i2000000002−22−20000i2−i2i2−i2000000000000
χ5722-2-2-22-22-200222−2−2000-22−2−2−222−2−222-220022-2-222-2-2202−22-200-220022−2−2−2−222000000002−2−2200002−2−22000000000000
χ5822-2-2-22-22-200222−2−2000-22−2−2−222−2−222-220022-2-22-222-202−2-22002-200−2−22222−2−2000000002−2−220000−222−2000000000000
χ5922-2-2-22-22-200222−2−2000-22−2−2−222−2−222-22002-222-22-2-2202−2-22002-200−2−22222−2−200000000−222−200002−2−22000000000000
χ6022-2-2-22-22-200222−2−2000-22−2−2−222−2−222-22002-222-2-222-202−22-200-220022−2−2−2−22200000000−222−20000−222−2000000000000
χ6122-2-2-22-22-2002−2−222000-2−2222−2−222−2−2-220022-2-222-2-220−222-200-2200−2−22222−2−200000000−222−20000−222−2000000000000
χ6222-2-2-22-22-2002−2−222000-2−2222−2−222−2−2-220022-2-22-222-20−22-22002-20022−2−2−2−22200000000−222−200002−2−22000000000000
χ6322-2-2-22-22-2002−2−222000-2−2222−2−222−2−2-22002-222-22-2-220−22-22002-20022−2−2−2−222000000002−2−220000−222−2000000000000
χ6422-2-2-22-22-2002−2−222000-2−2222−2−222−2−2-22002-222-2-222-20−222-200-2200−2−22222−2−2000000002−2−2200002−2−22000000000000
χ65444444444-4-440000-4-4-4-40000000000-4-444-400000000400000000000000000000000000000000000000000000000000
χ66444444-4-4-444-44444-4-440-4-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ67444444-4-4-444-4-4-4-4-4-4-44044-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ68444444-4-4-4-4-4-4000044-4000000000000000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ69444444-4-4-4-4-4-4000044-400000000000000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ704444-4-44-4-444444444-4-40-4-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ714444-4-44-4-4444-4-4-4-44-4-40444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ724444-4-44-4-4-4-440000-4440000000000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ734444-4-44-4-4-4-440000-44400000000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ744444-4-4-444-4-4-400004-44-4000000000044-4-4-400000000400000000000000000000000000000000000000000000000000
χ7544-4-44-444-400-42222−22−22000422−222222−22−22−22−222222-4400-4000000000−2222000000000000000000000000000000000000000000000000
χ7644-4-44-444-400-4−22−2222220004−2222−22−2222222222−22−22-4400-400000000022−22000000000000000000000000000000000000000000000000
χ7744-4-44-4-4-440042222−22−220000−222222−22−2222000000000000000000000022−220022−222-2-222-2-2200000000000000000000000000000000
χ7844-4-44-4-4-440042222−22−220000−222222−22−22220000000000000000000000−222200−2222-222-2-222-200000000000000000000000000000000
χ7944-4-44-4-4-44004−22−222222000022−22−222222−22000000000000000000000022−220022−22-222-2-222-200000000000000000000000000000000
χ8044-4-44-4-4-44004−22−222222000022−22−222222−220000000000000000000000−222200−22222-2-222-2-2200000000000000000000000000000000
χ8144-4-4-444-4400-42222−22−220000−2222−222222−2200000000000000000000002i2−2i200−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ8244-4-4-444-4400-42222−22−220000−2222−222222−220000000000000000000000−2i22i2002i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ8344-4-4-444-4400-4−22−222222000022−2222−22−222200000000000000000000002i2−2i200−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ8444-4-4-444-4400-4−22−222222000022−2222−22−22220000000000000000000000−2i22i2002i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ8544-4-4-44-44-40042222−22−22000422−22−22−2222222222−22−224-400-4000000000−2222000000000000000000000000000000000000000000000000
χ8644-4-4-44-44-4004−22−2222220004−22222222−22−22−22−2222224-400-400000000022−22000000000000000000000000000000000000000000000000
χ878-88-80000000042−4242−4200000000004-44-40042−42000000000000000000000000000000000000000000000000000000000000
χ888-88-80000000042−4242−420000000000-44-4400−4242000000000000000000000000000000000000000000000000000000000000
χ898-88-800000000−4242−424200000000004-44-400−4242000000000000000000000000000000000000000000000000000000000000
χ908-88-800000000−4242−42420000000000-44-440042−42000000000000000000000000000000000000000000000000000000000000
χ918-8-88000008-800000000000000042−42−42420000000000000000000000000000000000000000000000000000000000000000
χ928-8-88000008-8000000000000000−424242−420000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800000-8808-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-8800000-880-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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