Finite Group Databasebeta

← Group #72309874

Character table — Group #72309874

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222224444444444444448888888888888888888888888888816161616161616161616161616161616161616161616161632323232323232323232
order122222444444888822224448888888822444488888888888888816161616161616164444888888881616161616161616161616164444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1111-1-1-1-111111-111-1-11-1-111-1-11111-1-1-1-1111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ6111111111111111111-1-1111-1-1-1-111111-111-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111111111-1-11111-1-111
χ7111111111111111111-1-1111-1-1-1-111111-111-1-11-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ8111111111111111111-1-1111-1-1-1-111111-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11111-1-1-1-11111111111-1-1-1-111-1-1
χ91111111111111111-1-111111-1-1-1-11111-11-1-1111-1-1-1-1111111-1-1-1-111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-111111-1-1-1-11111-11-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-1111111-1-1-1-11111
χ111111111111111111-1-111111-1-1-1-11111-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ121111111111111111-1-111111-1-1-1-11111-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1
χ131111111111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ151111111111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ171111-1-1111-11-1111111111-1-111-1-1-1-111-1-11-11-1-11-11111ii−i−i11-1-11111-1-1-1-1ii−i−ii−i-1-1ii−i−i11-1-111-1-111-1-1i−ii−ii−ii−ii−i
χ181111-1-1111-11-1111111111-1-111-1-1-1-111-1-11-11-1-11-11111ii−i−i11-1-1-1-1-1-11111−i−iiii−i-1-1ii−i−i-1-111-1-111-1-111−ii−iii−ii−i−ii
χ191111-1-1111-11-1111111111-1-111-1-1-1-111-1-11-11-1-11-11111−i−iii11-1-11111-1-1-1-1−i−iii−ii-1-1−i−iii11-1-111-1-111-1-1−ii−ii−ii−ii−ii
χ201111-1-1111-11-1111111111-1-111-1-1-1-111-1-11-11-1-11-11111−i−iii11-1-1-1-1-1-11111ii−i−i−ii-1-1−i−iii-1-111-1-111-1-111i−ii−i−ii−iii−i
χ211111-1-1111-11-1111111-1-11-1-1-1-111-1-111-111-1-11-1-1111-1-1ii−i−i-1-1111111-1-1-1-1ii−i−ii−i-11−i−iii11-1-1-1-111-1-111i−i−iii−i−ii−ii
χ221111-1-1111-11-1111111-1-11-1-1-1-111-1-111-111-1-11-1-1111-1-1ii−i−i-1-111-1-1-1-11111−i−iiii−i-11−i−iii-1-11111-1-111-1-1−iii−ii−i−iii−i
χ231111-1-1111-11-1111111-1-11-1-1-1-111-1-111-111-1-11-1-1111-1-1−i−iii-1-1111111-1-1-1-1−i−iii−ii-11ii−i−i11-1-1-1-111-1-111−iii−i−iii−ii−i
χ241111-1-1111-11-1111111-1-11-1-1-1-111-1-111-111-1-11-1-1111-1-1−i−iii-1-111-1-1-1-11111ii−i−i−ii-11ii−i−i-1-11111-1-111-1-1i−i−ii−iii−i−ii
χ251111-1-1111-11-11111-1-1111-1-1-1-111-1-1111-1-111-1-1-11-1-111ii−i−i-1-1111111-1-1-1-1ii−i−ii−i1-1−i−iii-1-11111-1-1-1-111−iii−i−iii−i−ii
χ261111-1-1111-11-11111-1-1111-1-1-1-111-1-1111-1-111-1-1-11-1-111ii−i−i-1-111-1-1-1-11111−i−iiii−i1-1−i−iii11-1-1-1-11111-1-1i−i−ii−iii−ii−i
χ271111-1-1111-11-11111-1-1111-1-1-1-111-1-1111-1-111-1-1-11-1-111−i−iii-1-1111111-1-1-1-1−i−iii−ii1-1ii−i−i-1-11111-1-1-1-111i−i−iii−i−iii−i
χ281111-1-1111-11-11111-1-1111-1-1-1-111-1-1111-1-111-1-1-11-1-111−i−iii-1-111-1-1-1-11111ii−i−i−ii1-1ii−i−i11-1-1-1-11111-1-1−iii−ii−i−ii−ii
χ291111-1-1111-11-11111-1-1-1-11-1-111-1-1-1-11111-11-11-11-1-1-1-1-1ii−i−i11-1-11111-1-1-1-1ii−i−ii−i11ii−i−i-1-111-1-11111-1-1−ii−ii−ii−iii−i
χ301111-1-1111-11-11111-1-1-1-11-1-111-1-1-1-11111-11-11-11-1-1-1-1-1ii−i−i11-1-1-1-1-1-11111−i−iiii−i11ii−i−i11-1-111-1-1-1-111i−ii−i−ii−ii−ii
χ311111-1-1111-11-11111-1-1-1-11-1-111-1-1-1-11111-11-11-11-1-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−iii−ii11−i−iii-1-111-1-11111-1-1i−ii−ii−ii−i−ii
χ321111-1-1111-11-11111-1-1-1-11-1-111-1-1-1-11111-11-11-11-1-1-1-1-1−i−iii11-1-1-1-1-1-11111ii−i−i−ii11−i−iii11-1-111-1-1-1-111−ii−iii−ii−ii−i
χ33222222222222-2-2-2-222222222222-2-2-2-2222222-222-2-2-2-20000-2-2-2-200000000000000-2-200000000000000000000000000
χ34222222222222-2-2-2-222-2-2222-2-2-2-2-2-2-2-22-222-2-2-2-2-2-2-2220000222200000000000000-2200000000000000000000000000
χ35222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-22-2-222-2-2-222-2-200002222000000000000002-200000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-22222220000-2-2-2-2000000000000002200000000000000000000000000
χ3722222222-2-2-2-200002222-22-222-2-2000022-2-2-2-20-22000000000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ3822222222-2-2-2-200002222-22-222-2-2000022-2-2-2-20-22000000000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ3922222222-2-2-2-2000022-2-2-22-2-2-22200002-2-2-22202-2000000000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ4022222222-2-2-2-2000022-2-2-22-2-2-22200002-2-2-22202-2000000000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ4122222222-2-2-2-20000-2-222-22-2-2-2220000-2222-2-202-2000000000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ4222222222-2-2-2-20000-2-222-22-2-2-2220000-2222-2-202-2000000000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ4322222222-2-2-2-20000-2-2-2-2-22-222-2-20000-2-222220-22000000000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4422222222-2-2-2-20000-2-2-2-2-22-222-2-20000-2-222220-22000000000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ45222222-2-2222222220000-2-2-2000022-2-2000000-2000000222200002-22-22-22-22-22-2-2-20000000000000000000000000000
χ46222222-2-2222222220000-2-2-2000022-2-2000000-200000022220000-22-22-22-22-22-22-2-20000000000000000000000000000
χ47222222-2-2222222220000-2-2-2000022-2-2000000-2000000-2-2-2-200002-22-22-22-2-22-22220000000000000000000000000000
χ48222222-2-2222222220000-2-2-2000022-2-2000000-2000000-2-2-2-20000-22-22-22-222-22-2220000000000000000000000000000
χ492222-2-2222-22-2-2-2-2-222222-2-222-2-222-2-2-2-22-22-222-2-2-2-2-20000-2-222000000000000002200000000000000000000000000
χ502222-2-2222-22-2-2-2-2-222-2-22-2-2-2-22222-2-2-222-2-222-22-2-222000022-2-2000000000000002-200000000000000000000000000
χ512222-2-2222-22-2-2-2-2-2-2-2222-2-2-2-22222-2-22-2-222-22-2222-2-2000022-2-200000000000000-2200000000000000000000000000
χ522222-2-2222-22-2-2-2-2-2-2-2-2-22-2-222-2-222-2-222-22-2222-222220000-2-22200000000000000-2-200000000000000000000000000
χ532222-2-222-22-2200002222-2-2222220000-2-2-22-220-2-2000000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ542222-2-222-22-2200002222-2-2222220000-2-2-22-220-2-2000000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ552222-2-222-22-22000022-2-2-2-22-2-2-2-20000-22-222-2022000000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ562222-2-222-22-22000022-2-2-2-22-2-2-2-20000-22-222-2022000000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ572222-2-222-22-220000-2-222-2-22-2-2-2-200002-22-2-22022000000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000
χ582222-2-222-22-220000-2-222-2-22-2-2-2-200002-22-2-22022000000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000
χ592222-2-222-22-220000-2-2-2-2-2-2222220000222-22-20-2-2000000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ602222-2-222-22-220000-2-2-2-2-2-2222220000222-22-20-2-2000000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ612222-2-2-2-22-22-222220000-2220000-2-2-2-200000020000002i2i−2i−2i00002-22-2-22-222i−2i−2i2i−2i2i0000000000000000000000000000
χ622222-2-2-2-22-22-222220000-2220000-2-2-2-200000020000002i2i−2i−2i0000-22-222-22-2−2i2i2i−2i−2i2i0000000000000000000000000000
χ632222-2-2-2-22-22-222220000-2220000-2-2-2-20000002000000−2i−2i2i2i00002-22-2-22-22−2i2i2i−2i2i−2i0000000000000000000000000000
χ642222-2-2-2-22-22-222220000-2220000-2-2-2-20000002000000−2i−2i2i2i0000-22-222-22-22i−2i−2i2i2i−2i0000000000000000000000000000
χ65444444-4-44444-4-4-4-40000-4-4-40000-4-444000000400000000000000000000000000000000000000000000000000000000
χ66444444-4-4-4-4-4-4000000004-44000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ67444444-4-4-4-4-4-4000000004-4400000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ684444-4-4-4-44-44-4-4-4-4-40000-44400004444000000-400000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-4-44-440000000044-4000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ704444-4-4-4-4-44-440000000044-400000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ7144-4-4004-400002i22i2−2i2−2i24-44-40004-400002i2−2i20000000002i2−2i22i2−2i200002i2−2i200000000000000000000000000000000000000000000
χ7244-4-4004-400002i22i2−2i2−2i24-4-44000-4400002i2−2i20000000002i2−2i2−2i22i20000−2i22i200000000000000000000000000000000000000000000
χ7344-4-4004-400002i22i2−2i2−2i2-444-4000-4400002i2−2i2000000000−2i22i22i2−2i20000−2i22i200000000000000000000000000000000000000000000
χ7444-4-4004-400002i22i2−2i2−2i2-44-440004-400002i2−2i2000000000−2i22i2−2i22i200002i2−2i200000000000000000000000000000000000000000000
χ7544-4-4004-40000−2i2−2i22i22i24-44-40004-40000−2i22i2000000000−2i22i2−2i22i20000−2i22i200000000000000000000000000000000000000000000
χ7644-4-4004-40000−2i2−2i22i22i24-4-44000-440000−2i22i2000000000−2i22i22i2−2i200002i2−2i200000000000000000000000000000000000000000000
χ7744-4-4004-40000−2i2−2i22i22i2-444-4000-440000−2i22i20000000002i2−2i2−2i22i200002i2−2i200000000000000000000000000000000000000000000
χ7844-4-4004-40000−2i2−2i22i22i2-44-440004-40000−2i22i20000000002i2−2i22i2−2i20000−2i22i200000000000000000000000000000000000000000000
χ794-4-444-400-444-44-44-4000000000004-40000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ804-4-444-400-444-44-44-4000000000004-4000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ814-4-444-400-444-4-44-4400000000000-440000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ824-4-444-400-444-4-44-4400000000000-44000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ834-4-44-4400-4-4444-44-400000000000-4400000000000000000000000000000000000000022−22−22220000000000000000000000
χ844-4-44-4400-4-4444-44-400000000000-44000000000000000000000000000000000000000−222222−220000000000000000000000
χ854-4-44-4400-4-444-44-44000000000004-40000000000000004-4-440000000000000000000000000000000000000000000000
χ864-4-44-4400-4-444-44-44000000000004-4000000000000000-444-40000000000000000000000000000000000000000000000
χ8788-8-800-8800004i24i2−4i2−4i20000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000
χ8888-8-800-880000−4i2−4i24i24i200000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000004i2−4i2−4i24i20000000004i2−4i2000000000000000000000004-4000000000000000000000000000000000000000000
χ908-88-8000000004i2−4i2−4i24i2000000000−4i24i200000000000000000000000-44000000000000000000000000000000000000000000
χ918-88-800000000−4i24i24i2−4i20000000004i2−4i200000000000000000000000-44000000000000000000000000000000000000000000
χ928-88-800000000−4i24i24i2−4i2000000000−4i24i2000000000000000000000004-4000000000000000000000000000000000000000000
χ938-8-888-8008-8-880000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-88-880088-8-80000000000000000000000000000000000000000000000000000000000000000000000000000000000

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