Finite Group Databasebeta

← Group #72319704

Character table — Group #72319704

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222224444444444444448888888888888888888888888888816161616161616161616161616161616161616161616161632323232323232323232
order122244444444888822244448888888824444488888888888888816161616161616162444444488881616161616161616161616162244888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ511111111111111111111-1-1111-1-1-1-111-111-11-1111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1
χ611111111111111111111-1-1111-1-1-1-111-111-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111111111-11-111111-1-1
χ711111111111111111111-1-1111-1-1-1-111-111-11-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-111
χ811111111111111111111-1-1111-1-1-1-111-111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1111111111-11-1-1-1-1-111
χ91111111111111111-1-11111111-1-1-1-1111-1-11-111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1111-1-1-1-11111-1-1-1-1-11-11-1-1-1-111
χ101111111111111111-1-11111111-1-1-1-1111-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111-11-111-1-111
χ111111111111111111-1-11111111-1-1-1-1111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-1-1-11111-1-1-1-11-11-11111-1-1
χ121111111111111111-1-11111111-1-1-1-1111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-11111-11-11-1-111-1-1
χ131111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ141111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ151111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ161111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ171111-1-11111-1-1-1-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i11-1-1ii−i−i11i−iii−i−iii−i−iii−i−i11-1-11-1i−ii−i
χ181111-1-11111-1-1-1-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-11-1ii−i−i11-1-1−i−i−i−iiiii-1-111ii−i−i11i−i−i−iii−i−iii−i−iii-1-111-11i−ii−i
χ191111-1-11111-1-1-1-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-11-1−i−iii11-1-1iiii−i−i−i−i-1-111−i−iii11−iiii−i−iii−i−iii−i−i-1-111-11−ii−ii
χ201111-1-11111-1-1-1-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-11-1−i−iii11-1-1−i−i−i−iiiii11-1-1−i−iii11−ii−i−iii−i−iii−i−iii11-1-11-1−ii−ii
χ211111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-11-1-11-1-111-11ii−i−i-1-111iiii−i−i−i−i11-1-1−i−iii1-1i−iii−i−i−i−iii−i−iii1-1-11-11i−i−ii
χ221111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-11-1-11-1-111-11ii−i−i-1-111−i−i−i−iiiii-1-111−i−iii1-1i−i−i−iiiii−i−iii−i−i-111-11-1i−i−ii
χ231111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-11-1-11-1-111-11−i−iii-1-111iiii−i−i−i−i-1-111ii−i−i1-1−iiii−i−i−i−iii−i−iii-111-11-1−iii−i
χ241111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-11-1-11-1-111-11−i−iii-1-111−i−i−i−iiiii11-1-1ii−i−i1-1−ii−i−iiiii−i−iii−i−i1-1-11-11−iii−i
χ251111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-111111-1-1-11ii−i−i-1-111iiii−i−i−i−i11-1-1−i−iii-11i−i−i−iiiii−i−i−i−iii-111-1-11−iii−i
χ261111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-111111-1-1-11ii−i−i-1-111−i−i−i−iiiii-1-111−i−iii-11i−iii−i−i−i−iiiii−i−i1-1-111-1−iii−i
χ271111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-111111-1-1-11−i−iii-1-111iiii−i−i−i−i-1-111ii−i−i-11−ii−i−iiiii−i−i−i−iii1-1-111-1i−i−ii
χ281111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-111111-1-1-11−i−iii-1-111−i−i−i−iiiii11-1-1ii−i−i-11−iiii−i−i−i−iiiii−i−i-111-1-11i−i−ii
χ291111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1111-1111111-1ii−i−i11-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1i−i−i−iii−i−iiiii−i−i-1-1111-1−ii−ii
χ301111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1111-1111111-1ii−i−i11-1-1−i−i−i−iiiii-1-111ii−i−i-1-1i−iii−i−iii−i−i−i−iii11-1-1-11−ii−ii
χ311111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1111-1111111-1−i−iii11-1-1iiii−i−i−i−i-1-111−i−iii-1-1−ii−i−iii−i−iiiii−i−i11-1-1-11i−ii−i
χ321111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1111-1111111-1−i−iii11-1-1−i−i−i−iiiii11-1-1−i−iii-1-1−iiii−i−iii−i−i−i−iii-1-1111-1i−ii−i
χ33222222222222-2-2-2-22222222-2-22222-2-2222222-2-2-2-2-2220000-2-2-2-20000000000000000-2-2000000000000000000000000
χ34222222222222-2-2-2-22222-2-22-2-2-2-2-2-2-2-2-222-22-2-2-2-222-2-2000022220000000000000000-22000000000000000000000000
χ35222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-22-2-22-22-222-2-2-2-20000222200000000000000002-2000000000000000000000000
χ36222222222222-2-2-2-2-2-222-2-22-2-22222-2-2-2-2-2-2-2-2-22222220000-2-2-2-2000000000000000022000000000000000000000000
χ3722222222-2-222222200-2-200-2220000-2-2000000-20000002222000022-2-222-2-22-2-22000000-2-20000000000000000000000
χ3822222222-2-222222200-2-200-2220000-2-2000000-200000022220000-2-222-2-222-222-2000000-2-20000000000000000000000
χ3922222222-2-222222200-2-200-2220000-2-2000000-2000000-2-2-2-2000022-2-222-2-2-222-2000000220000000000000000000000
χ4022222222-2-222222200-2-200-2220000-2-2000000-2000000-2-2-2-20000-2-222-2-2222-2-22000000220000000000000000000000
χ41222222-2-222-2-2000022-2222-20022-2-200-2-2-222-200000-2200000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ42222222-2-222-2-2000022-2222-20022-2-200-2-2-222-200000-2200000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ43222222-2-222-2-2000022-22-2-2-200-2-222002-2-2-222000002-200000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ44222222-2-222-2-2000022-22-2-2-200-2-222002-2-2-222000002-200000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ45222222-2-222-2-20000-2-2-2222-200-2-22200-2222-2-2000002-200000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ46222222-2-222-2-20000-2-2-2222-200-2-22200-2222-2-2000002-200000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ47222222-2-222-2-20000-2-2-22-2-2-20022-2-200222-2-2200000-2200000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ48222222-2-222-2-20000-2-2-22-2-2-20022-2-200222-2-2200000-2200000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ492222-2-22222-2-2222222-2-2222-2-222-2-222-22-2-2-22-222222-20000-2-2220000000000000000-2-2000000000000000000000000
χ502222-2-22222-2-2222222-2-2-2-22-2-2-2-2222222-22-2-2-222-2-2-22000022-2-20000000000000000-22000000000000000000000000
χ512222-2-22222-2-22222-2-2-2-2222-2-2-2-22222-2-22-222-2-2-222-22000022-2-200000000000000002-2000000000000000000000000
χ522222-2-22222-2-22222-2-2-2-2-2-22-2-222-2-2222-2222-2-2-2-2-2-22-20000-2-222000000000000000022000000000000000000000000
χ532222-2-222-2-2-2-2-2-2-2-2002200-222000022000000-20000002i2i−2i−2i00002i2i−2i−2i−2i−2i2i2i2-22-2000000−2i2i0000000000000000000000
χ542222-2-222-2-2-2-2-2-2-2-2002200-222000022000000-20000002i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i-22-22000000−2i2i0000000000000000000000
χ552222-2-222-2-2-2-2-2-2-2-2002200-222000022000000-2000000−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i-22-220000002i−2i0000000000000000000000
χ562222-2-222-2-2-2-2-2-2-2-2002200-222000022000000-2000000−2i−2i2i2i0000−2i−2i2i2i2i2i−2i−2i2-22-20000002i−2i0000000000000000000000
χ572222-2-2-2-222220000222-222-2002222002-22-2-2-200000-2-2000000002−22−2−22−220000000000002−2−222−2−222−2−220000000000
χ582222-2-2-2-222220000222-222-2002222002-22-2-2-200000-2-200000000−22−222−22−2000000000000−222−2−222−2−222−20000000000
χ592222-2-2-2-222220000222-2-2-2-200-2-2-2-200-2-222-220000022000000002−22−2−22−220000000000002−2−22−222−2−222−20000000000
χ602222-2-2-2-222220000222-2-2-2-200-2-2-2-200-2-222-22000002200000000−22−222−22−2000000000000−222−22−2−222−2−220000000000
χ612222-2-2-2-222220000-2-22-222-200-2-2-2-20022-2-22-20000022000000002−22−2−22−22000000000000−222−22−2−22−222−20000000000
χ622222-2-2-2-222220000-2-22-222-200-2-2-2-20022-2-22-2000002200000000−22−222−22−20000000000002−2−22−222−22−2−220000000000
χ632222-2-2-2-222220000-2-22-2-2-2-200222200-22-222200000-2-2000000002−22−2−22−22000000000000−222−2−222−22−2−220000000000
χ642222-2-2-2-222220000-2-22-2-2-2-200222200-22-222200000-2-200000000−22−222−22−20000000000002−2−222−2−22−222−20000000000
χ6544444444-4-444-4-4-4-400-4-400-4-4-4000044000000400000000000000000000000000000000000000000000000000000000
χ66444444-4-4-4-4-4-40000004-4004000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ67444444-4-4-4-4-4-40000004-400400000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ684444-4-444-4-4-4-44444004400-4-4-40000-4-4000000400000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-4-4-444000000-440040000000000000000000000000000022−22−2222−222222−220000000000000000000000000000000000
χ704444-4-4-4-4-4-444000000-4400400000000000000000000000000000−222222−2222−22−22220000000000000000000000000000000000
χ7144-4-400004-4002i22i2−2i2−2i24-4004-40004-4002i2−2i200000002i2−2i22i2−2i2000000002i2−2i2000000000000000000000000000000000000000000
χ7244-4-400004-4002i22i2−2i2−2i24-400-44000-44002i2−2i200000002i2−2i2−2i22i200000000−2i22i2000000000000000000000000000000000000000000
χ7344-4-400004-4002i22i2−2i2−2i2-44004-4000-44002i2−2i20000000−2i22i22i2−2i200000000−2i22i2000000000000000000000000000000000000000000
χ7444-4-400004-4002i22i2−2i2−2i2-4400-440004-4002i2−2i20000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000000000000000000
χ7544-4-400004-400−2i2−2i22i22i24-4004-40004-400−2i22i20000000−2i22i2−2i22i200000000−2i22i2000000000000000000000000000000000000000000
χ7644-4-400004-400−2i2−2i22i22i24-400-44000-4400−2i22i20000000−2i22i22i2−2i2000000002i2−2i2000000000000000000000000000000000000000000
χ7744-4-400004-400−2i2−2i22i22i2-44004-4000-4400−2i22i200000002i2−2i2−2i22i2000000002i2−2i2000000000000000000000000000000000000000000
χ7844-4-400004-400−2i2−2i22i22i2-4400-440004-400−2i22i200000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000000000000000000
χ794-44-44i−4i4-4004i−4i4i−4i4i−4i00000004-40000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ804-44-44i−4i4-4004i−4i4i−4i4i−4i00000004-4000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ814-44-44i−4i4-4004i−4i−4i4i−4i4i0000000-4400000000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000
χ824-44-44i−4i4-4004i−4i−4i4i−4i4i0000000-440000000000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000
χ834-44-4−4i4i4-400−4i4i4i−4i4i−4i0000000-4400000000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000
χ844-44-4−4i4i4-400−4i4i4i−4i4i−4i0000000-440000000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000
χ854-44-4−4i4i4-400−4i4i−4i4i−4i4i00000004-40000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ864-44-4−4i4i4-400−4i4i−4i4i−4i4i00000004-4000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ8788-8-80000-88004i24i2−4i2−4i20000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000
χ8888-8-80000-8800−4i2−4i24i24i200000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000
χ898-88-88i−8i-8800−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i-88008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000000042−42−42420000000000042−4200000000000000000004-400000000000000000000000000000000000000000000
χ928-8-880000000042−42−424200000000000−42420000000000000000000-4400000000000000000000000000000000000000000000
χ938-8-8800000000−424242−420000000000042−420000000000000000000-4400000000000000000000000000000000000000000000
χ948-8-8800000000−424242−4200000000000−424200000000000000000004-400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.