Finite Group Databasebeta

← Group #72319921

Character table — Group #72319921

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222224444444444444448888888888888888888888888888816161616161616161616161616161616161616161616161632323232323232323232
order122244444444888822222448888888844444488888888888888816161616161616162244888888881616161616161616161616162244888888
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
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ51111111111111111111-1-111-1-111-1-11111-1-11-1-1111-1-1-11111-1-1-1-11111111111111-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-1
χ61111111111111111111-1-111-1-111-1-11111-1-11-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111111111-11-111111-1-1
χ71111111111111111111-1-111-1-111-1-11111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-111
χ81111111111111111111-1-111-1-111-1-11111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1111111111-11-1-1-1-1-111
χ911111111111111111-1-11111-1-111-1-111-1-111-11-11-1-111-11111-1-1-1-1111111111111-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-1-111
χ1011111111111111111-1-11111-1-111-1-111-1-111-11-11-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111-11-111-1-111
χ1111111111111111111-1-11111-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-1
χ1211111111111111111-1-11111-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111111111-1-1-1-11111-11-11-1-111-1-1
χ1311111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ1411111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ1511111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ1611111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ171111-1-11111-1-1-1-1-1-1-111111-1-1-11111-1-11-11-1-1-111-1-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-11-111i−iii−i−iii−i−iii−i−iii−i−i1-1-111-1i−ii−i
χ181111-1-11111-1-1-1-1-1-1-111111-1-1-11111-1-11-11-1-1-111-1-1-1-1-1ii−i−i11-1-1−i−i−i−iiiii-11-1111i−iii−i−i−i−iii−i−iii−i−iii-111-1-11i−ii−i
χ191111-1-11111-1-1-1-1-1-1-111111-1-1-11111-1-11-11-1-1-111-1-1-1-1-1−i−iii11-1-1iiii−i−i−i−i-11-1111−ii−i−iiiii−i−iii−i−iii−i−i-111-1-11−ii−ii
χ201111-1-11111-1-1-1-1-1-1-111111-1-1-11111-1-11-11-1-1-111-1-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-11-111−ii−i−iii−i−iii−i−iii−i−iii1-1-111-1−ii−ii
χ211111-1-11111-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-1-11-11-11-1-1111ii−i−i-1-111iiii−i−i−i−i1-11-11-1i−i−i−iiiii−i−i−i−iii−i−iii11-1-1-11i−i−ii
χ221111-1-11111-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-1-11-11-11-1-1111ii−i−i-1-111−i−i−i−iiiii-11-111-1i−i−i−iii−i−iiiii−i−iii−i−i-1-1111-1i−i−ii
χ231111-1-11111-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-1-11-11-11-1-1111−i−iii-1-111iiii−i−i−i−i-11-111-1−iiii−i−iii−i−i−i−iii−i−iii-1-1111-1−iii−i
χ241111-1-11111-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-1-11-11-11-1-1111−i−iii-1-111−i−i−i−iiiii1-11-11-1−iiii−i−i−i−iiiii−i−iii−i−i11-1-1-11−iii−i
χ251111-1-11111-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-111-11-1-1111-1-11ii−i−i-1-111iiii−i−i−i−i1-11-1-11i−i−i−iii−i−iiiii−i−i−i−iii-1-111-11−iii−i
χ261111-1-11111-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-111-11-1-1111-1-11ii−i−i-1-111−i−i−i−iiiii-11-11-11i−i−i−iiiii−i−i−i−iiiii−i−i11-1-11-1−iii−i
χ271111-1-11111-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-111-11-1-1111-1-11−i−iii-1-111iiii−i−i−i−i-11-11-11−iiii−i−i−i−iiiii−i−i−i−iii11-1-11-1i−i−ii
χ281111-1-11111-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-111-11-1-1111-1-11−i−iii-1-111−i−i−i−iiiii1-11-1-11−iiii−i−iii−i−i−i−iiiii−i−i-1-111-11i−i−ii
χ291111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11-1111111111-1ii−i−i11-1-1iiii−i−i−i−i1-11-1-1-1i−iii−i−i−i−iii−i−iiiii−i−i-111-11-1−ii−ii
χ301111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11-1111111111-1ii−i−i11-1-1−i−i−i−iiiii-11-11-1-1i−iii−i−iii−i−iii−i−i−i−iii1-1-11-11−ii−ii
χ311111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11-1111111111-1−i−iii11-1-1iiii−i−i−i−i-11-11-1-1−ii−i−iii−i−iii−i−iiiii−i−i1-1-11-11i−ii−i
χ321111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11-1111111111-1−i−iii11-1-1−i−i−i−iiiii1-11-1-1-1−ii−i−iiiii−i−iii−i−i−i−iii-111-11-1i−ii−i
χ33222222222222-2-2-2-2222222222-2-222-2-22222222-2-2-2-2-220000-2-2-2-2000000000000-2-20000000000000000000000000000
χ34222222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-222-2-22-2-2-2-2-222-200002222000000000000-220000000000000000000000000000
χ35222222222222-2-2-2-22-2-22222-2-2-2-2-2-2-2-2-2-222-22-2-222-2-2-2000022220000000000002-20000000000000000000000000000
χ36222222222222-2-2-2-22-2-2-2-22222-2-222-2-2-2-2-2-2-2-22-2222220000-2-2-2-2000000000000220000000000000000000000000000
χ372222222-2-22-2-2000022222-2-2-2-2002200-2-2-2-222-200000200000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ382222222-2-22-2-2000022222-2-2-2-2002200-2-2-2-222-200000200000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ392222222-2-22-2-20000222-2-2-2-22200-2-200-2-2222-2200000-200000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ402222222-2-22-2-20000222-2-2-2-22200-2-200-2-2222-2200000-200000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ412222222-2-22-2-200002-2-222-2-22200-2-20022-2-2-22200000-200000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ422222222-2-22-2-200002-2-222-2-22200-2-20022-2-2-22200000-200000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ432222222-2-22-2-200002-2-2-2-2-2-2-2-20022002222-2-2-200000200000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ442222222-2-22-2-200002-2-2-2-2-2-2-2-20022002222-2-2-200000200000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ45222222-222-2222222-20000-2-2002200-2-20000000-200000222200002-22-22-22-22-2-2200-2-200000000000000000000000000
χ46222222-222-2222222-20000-2-2002200-2-20000000-20000022220000-22-22-22-22-222-200-2-200000000000000000000000000
χ47222222-222-2222222-20000-2-2002200-2-20000000-200000-2-2-2-200002-22-22-22-2-222-2002200000000000000000000000000
χ48222222-222-2222222-20000-2-2002200-2-20000000-200000-2-2-2-20000-22-22-22-222-2-22002200000000000000000000000000
χ492222-2-22222-2-22222-222222-2-2-2-2-222222-22-2-2-22-22222-20000-2-222000000000000-2-20000000000000000000000000000
χ502222-2-22222-2-22222-222-2-22-222-2-2-2-2222-2-22-22-2-222-2-22000022-2-2000000000000-220000000000000000000000000000
χ512222-2-22222-2-22222-2-2-2222-222-2-2-2-222-222-22-2-2-2-2-2222000022-2-20000000000002-20000000000000000000000000000
χ522222-2-22222-2-22222-2-2-2-2-22-2-2-2-2-22222-22-22222-2-2-2-2-2-20000-2-222000000000000220000000000000000000000000000
χ532222-2-22-2-22220000-22222-2222002200-22-22-2-2-200000-20000000022−2−2−2−2220000000000002−2−222−2−222−2−220000000000
χ542222-2-22-2-22220000-22222-2222002200-22-22-2-2-200000-200000000−2−22222−2−2000000000000−222−2−222−2−222−20000000000
χ552222-2-22-2-22220000-222-2-2-22-2-200-2-200-222-2-2220000020000000022−2−2−2−2220000000000002−2−22−222−2−222−20000000000
χ562222-2-22-2-22220000-222-2-2-22-2-200-2-200-222-2-22200000200000000−2−22222−2−2000000000000−222−22−2−222−2−220000000000
χ572222-2-22-2-22220000-2-2-222-22-2-200-2-2002-2-222-220000020000000022−2−2−2−222000000000000−222−22−2−22−222−20000000000
χ582222-2-22-2-22220000-2-2-222-22-2-200-2-2002-2-222-2200000200000000−2−22222−2−20000000000002−2−22−222−22−2−220000000000
χ592222-2-22-2-22220000-2-2-2-2-2-22220022002-22-222-200000-20000000022−2−2−2−222000000000000−222−2−222−22−2−220000000000
χ602222-2-22-2-22220000-2-2-2-2-2-22220022002-22-222-200000-200000000−2−22222−2−20000000000002−2−222−2−22−222−20000000000
χ612222-2-2-222-2-2-2-2-2-2-220000-22002200220000000-2000002i2i−2i−2i00002i−2i2i−2i−2i2i−2i2i22-2-200−2i2i00000000000000000000000000
χ622222-2-2-222-2-2-2-2-2-2-220000-22002200220000000-2000002i2i−2i−2i0000−2i2i−2i2i2i−2i2i−2i-2-22200−2i2i00000000000000000000000000
χ632222-2-2-222-2-2-2-2-2-2-220000-22002200220000000-200000−2i−2i2i2i00002i−2i2i−2i−2i2i−2i2i-2-222002i−2i00000000000000000000000000
χ642222-2-2-222-2-2-2-2-2-2-220000-22002200220000000-200000−2i−2i2i2i0000−2i2i−2i2i2i−2i2i−2i22-2-2002i−2i00000000000000000000000000
χ65444444-444-444-4-4-4-4-40000-4-400-4-40044000000040000000000000000000000000000000000000000000000000000000
χ66444444-4-4-4-4-4-40000-4000044000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ67444444-4-4-4-4-4-40000-400004400000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ684444-4-4-444-4-4-4444440000-4400-4-400-4-4000000040000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-4-4-4440000400004-40000000000000000000000000000022−22−2222−222222−220000000000000000000000000000000000
χ704444-4-4-4-4-4-4440000400004-400000000000000000000000000000−222222−2222−22−22220000000000000000000000000000000000
χ7144-4-44i−4i04-404i−4i4i4i−4i−4i0000000004-4000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ7244-4-44i−4i04-404i−4i4i4i−4i−4i0000000004-400000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ7344-4-44i−4i04-404i−4i−4i−4i4i4i000000000-44000000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000
χ7444-4-44i−4i04-404i−4i−4i−4i4i4i000000000-4400000000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000
χ7544-4-4−4i4i04-40−4i4i4i4i−4i−4i000000000-44000000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000
χ7644-4-4−4i4i04-40−4i4i4i4i−4i−4i000000000-4400000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000
χ7744-4-4−4i4i04-40−4i4i−4i−4i4i4i0000000004-4000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ7844-4-4−4i4i04-40−4i4i−4i−4i4i4i0000000004-400000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ794-4-4400-40040022−2222−2204-44-40000004-422−220000000022−2222−22000000022−22000000000000000000000000000000000000000000
χ804-4-4400-40040022−2222−2204-4-44000000-4422−220000000022−22−22220000000−2222000000000000000000000000000000000000000000
χ814-4-4400-40040022−2222−220-444-4000000-4422−2200000000−222222−220000000−2222000000000000000000000000000000000000000000
χ824-4-4400-40040022−2222−220-44-440000004-422−2200000000−2222−2222000000022−22000000000000000000000000000000000000000000
χ834-4-4400-400400−2222−222204-44-40000004-4−222200000000−2222−22220000000−2222000000000000000000000000000000000000000000
χ844-4-4400-400400−2222−222204-4-44000000-44−222200000000−222222−22000000022−22000000000000000000000000000000000000000000
χ854-4-4400-400400−2222−22220-444-4000000-44−22220000000022−22−2222000000022−22000000000000000000000000000000000000000000
χ864-4-4400-400400−2222−22220-44-440000004-4−22220000000022−2222−220000000−2222000000000000000000000000000000000000000000
χ8788-8-88i−8i0-880−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i8i0-8808i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000004i2−4i2−4i24i2000000042−42000000000000000000000004i−4i00000000000000000000000000000000000000000000
χ908-88-8000000004i2−4i2−4i24i20000000−424200000000000000000000000−4i4i00000000000000000000000000000000000000000000
χ918-88-800000000−4i24i24i2−4i2000000042−4200000000000000000000000−4i4i00000000000000000000000000000000000000000000
χ928-88-800000000−4i24i24i2−4i20000000−4242000000000000000000000004i−4i00000000000000000000000000000000000000000000
χ938-8-8800800-80042−4242−420000000000000−4242000000000000000000000000000000000000000000000000000000000000000
χ948-8-8800800-800−4242−4242000000000000042−42000000000000000000000000000000000000000000000000000000000000000

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