Finite Group Databasebeta

← Group #72342547

Character table — Group #72342547

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222222244444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222444444444424444444888888884444444444444444888822224444444488881616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−ii−ii−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ10111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−ii−ii−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ11111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-111ii−i−i−ii−iiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ12111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-111ii−i−i−ii−ii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ13111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-111−i−iiii−ii−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ14111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-111−i−iiii−ii−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ15111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−ii−iiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ16111111-1-111-1-111-111-1-1111-1-1-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−ii−ii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ171111-1-111-1-1-1-1111111-11-1-11-1-111-1-11111111-1-111-1-111-1-111-1-11-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-111-1-1-1-1111111-11-1-11-1-111-1-11111111-1-111-1-111-1-111-1-11-1-1-11111-1-1-1-11-11-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ191111-1-111-1-1-1-1111111-11-1-11-1-111-1-11111111-1-111-1-1-1-111-1-1111-1-1-1-1-1-1-111111-11-1-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ201111-1-111-1-1-1-1111111-11-1-11-1-111-1-11111111-1-111-1-1-1-111-1-1111-1-1-1-1-1-1-111111-11-1-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ211111-1-111-1-1-1-1111111-11-1-11-1-111-1-111111-1-111-1-11111-1-111-1-11-1-1-1-1-1-1-11111-11-1111-1-111-1-111-1-111-1-111-1-1-11-11-11-11
χ221111-1-111-1-1-1-1111111-11-1-11-1-111-1-111111-1-111-1-11111-1-111-1-11-1-1-1-1-1-1-11111-11-1111-1-1-1-111-1-111-1-111-1-1111-11-11-11-1
χ231111-1-111-1-1-1-1111111-11-1-11-1-111-1-111111-1-111-1-111-1-111-1-1111-1-1-11111-1-1-1-1-11-11-1-11111-1-111-1-1-1-111-1-111-11-111-11-1
χ241111-1-111-1-1-1-1111111-11-1-11-1-111-1-111111-1-111-1-111-1-111-1-1111-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-11111-1-111-1-11-11-1-11-11
χ251111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-11111-1-1-1-111i−i−iii−i−iiii−i−i−i−iii11-1-1-1-1111-1-11i−i−ii
χ261111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-11111-1-1-1-111i−i−iii−i−ii−i−iiiii−i−i-1-11111-1-1-111-1−iii−i
χ271111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11ii−i−i−i−iii−i−iiiii−i−i1-111-1-11111-1-1i−i−ii−iii−iii−i−i−i−iii-1-11111-1-11-1-11−iii−i
χ281111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11ii−i−i−i−iii−i−iiiii−i−i1-111-1-11111-1-1i−i−ii−iii−i−i−iiiii−i−i11-1-1-1-111-111-1i−i−ii
χ291111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11−i−iiiii−i−iii−i−i−i−iii1-111-1-11111-1-1−iii−ii−i−iiii−i−i−i−iii11-1-1-1-111-111-1−iii−i
χ301111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11−i−iiiii−i−iii−i−i−i−iii1-111-1-11111-1-1−iii−ii−i−ii−i−iiiii−i−i-1-11111-1-11-1-11i−i−ii
χ311111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-11111-1-1-1-111−iii−i−iii−iii−i−i−i−iii-1-11111-1-1-111-1i−i−ii
χ321111-1-1-1-1-1-11111-111-111-1-1-111-11-1-1-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-11111-1-1-1-111−iii−i−iii−i−i−iiiii−i−i11-1-1-1-1111-1-11−iii−i
χ3322222222222222222222222222-2-2-2-2-2-2-2-20000000022222222-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ3422222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ3522222222-2-2-2-2222-2-222-22-2-22-2-222222-2-2222-2-222-2-200000000-2-22-200000000-22-220000000000000000000000000000
χ3622222222-2-2-2-2222-2-222-22-2-22-2-222222-2-22-2-222-2-22200000000-2-22-2000000002-22-20000000000000000000000000000
χ3722222222-2-2-2-2222-2-222-22-2-22-2-2-2-2-2-2-222-2000000000000000022-222-22-22-22-200000000000000000000000000000000
χ3822222222-2-2-2-2222-2-222-22-2-22-2-2-2-2-2-2-222-2000000000000000022-22-22-22-22-2200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222-222-22-200000000000000002-22-22-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-222-22-200000000000000002-22-22-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ4122222222-2-2-2-2-2-2-2-2-2-222-222-22-20000000000000000-22-22-22-2200000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4222222222-2-2-2-2-2-2-2-2-2-222-222-22-20000000000000000-22-22-22-2200000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ43222222-2-222-2-222-222-2-2222-2-2-2-2-2-2-22222-2000000002i2i2i2i−2i−2i−2i−2i-2-222000000000000−2i2i−2i2i000000000000000000000000
χ44222222-2-222-2-222-222-2-2222-2-2-2-2-2-2-22222-200000000−2i−2i−2i−2i2i2i2i2i-2-2220000000000002i−2i2i−2i000000000000000000000000
χ45222222-2-2-2-22222-2-2-2-2-2-22-22-222222-2-22222i2i−2i−2i−2i−2i2i2i00000000-2-2-2200000000−2i2i2i−2i0000000000000000000000000000
χ46222222-2-2-2-22222-2-2-2-2-2-22-22-222222-2-2222−2i−2i2i2i2i2i−2i−2i00000000-2-2-22000000002i−2i−2i2i0000000000000000000000000000
χ47222222-2-2-2-22222-2-2-2-2-2-22-22-222-2-2-222-2-2-20000000000000000222-22-2-222-2-2200000000000000000000000000000000
χ48222222-2-2-2-22222-2-2-2-2-2-22-22-222-2-2-222-2-2-20000000000000000222-2-222-2-222-200000000000000000000000000000000
χ49222222-2-2-2-222-2-22-2-22-22-22-22-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ50222222-2-2-2-222-2-22-2-22-22-22-22-2200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ51222222-2-2-2-222-2-22-2-22-22-22-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ52222222-2-2-2-222-2-22-2-22-22-22-22-220000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ532222-2-2222222222-2-22-2-2-22-2-22-22-2-222-2-222222222200000000-22-2200000000-2-2-2-20000000000000000000000000000
χ542222-2-2222222222-2-22-2-2-22-2-22-22-2-222-2-22-2-2-2-2-2-2-2-200000000-22-220000000022220000000000000000000000000000
χ552222-2-2222222222-2-22-2-2-22-2-22-2-222-2-222-200000000000000002-22-22-22-2-22-2200000000000000000000000000000000
χ562222-2-2222222222-2-22-2-2-22-2-22-2-222-2-222-200000000000000002-22-2-22-222-22-200000000000000000000000000000000
χ572222-2-2222222-2-2-2-2-2-2-222-222-2-200000000000000002-2-222-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ582222-2-2222222-2-2-2-2-2-2-222-222-2-200000000000000002-2-222-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ592222-2-2222222-2-2-2-2-2-2-222-222-2-20000000000000000-222-2-222-200000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ602222-2-2222222-2-2-2-2-2-2-222-222-2-20000000000000000-222-2-222-200000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ612222-2-222-2-2-2-2222222-22-2-22-2-22-222-2-2-2-2-20000000022-2-222-2-2-2222000000000000-2-222000000000000000000000000
χ622222-2-222-2-2-2-2222222-22-2-22-2-22-222-2-2-2-2-200000000-2-222-2-222-222200000000000022-2-2000000000000000000000000
χ632222-2-2-2-222-2-222-2-2-2-22-2-2222-222-2-2-2-22222i2i2i2i−2i−2i−2i−2i00000000-222-200000000−2i−2i2i2i0000000000000000000000000000
χ642222-2-2-2-222-2-222-2-2-2-22-2-2222-222-2-2-2-2222−2i−2i−2i−2i2i2i2i2i00000000-222-2000000002i2i−2i−2i0000000000000000000000000000
χ652222-2-2-2-222-2-222-2-2-2-22-2-2222-22-22222-2-2-200000000000000002-2-222-2-22-222-200000000000000000000000000000000
χ662222-2-2-2-222-2-222-2-2-2-22-2-2222-22-22222-2-2-200000000000000002-2-22-222-22-2-2200000000000000000000000000000000
χ672222-2-2-2-222-2-2-2-22-2-22222-2-2-22200000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ682222-2-2-2-222-2-2-2-22-2-22222-2-2-22200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ692222-2-2-2-222-2-2-2-22-2-22222-2-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ702222-2-2-2-222-2-2-2-22-2-22222-2-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ712222-2-2-2-2-2-22222-222-222-2-2-222-2-2222222-2000000002i2i−2i−2i−2i−2i2i2i-22-2-2000000000000−2i2i2i−2i000000000000000000000000
χ722222-2-2-2-2-2-22222-222-222-2-2-222-2-2222222-200000000−2i−2i2i2i2i2i−2i−2i-22-2-20000000000002i−2i−2i2i000000000000000000000000
χ73444444444444-4-4-444-44-4-4-4-4-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-444-4-4-4-44444-4-4-4-4444-400000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-4-4-4-4-4-4-444-4-4-444-444400000000000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-4-4-444-4-444444-4444-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ7744-4-4004-400004-4400-4000000004004-400-44-4004-4000000000000000000000000000000000000000000000000000000
χ7844-4-4004-400004-4400-4000000004004-400-4-4400-44000000000000000000000000000000000000000000000000000000
χ7944-4-4004-400004-4400-400000000-400-44004004i−4i004i−4i0000000000000000000000000000000000000000000000000000
χ8044-4-4004-400004-4400-400000000-400-4400400−4i4i00−4i4i0000000000000000000000000000000000000000000000000000
χ8144-4-400-4400004-4-400400000000400-4400-44i−4i00−4i4i000000000000000000000000000000000000000000000000000000
χ8244-4-400-4400004-4-400400000000400-4400-4−4i4i004i−4i000000000000000000000000000000000000000000000000000000
χ8344-4-400-4400004-4-400400000000-4004-4004004-400-440000000000000000000000000000000000000000000000000000
χ8444-4-400-4400004-4-400400000000-4004-400400-44004-40000000000000000000000000000000000000000000000000000
χ8588-8-8008-80000-88-80080000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-880000-88800-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ878-88-80000008i−8i0000000000000004i2−4i20042−420000000000000000000000000000000000000000000000000000000000000
χ888-88-80000008i−8i000000000000000−4i24i200−42420000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000−8i8i0000000000000004i2−4i200−42420000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000−8i8i000000000000000−4i24i20042−420000000000000000000000000000000000000000000000000000000000000
χ918-8-888-8008-8000008-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-888-800-8800000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-88-88008-800000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-88-8800-88000008-800000000000000000000000000000000000000000000000000000000000000000000000000000

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