Finite Group Databasebeta

← Group #72317758

Character table — Group #72317758

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222224444444444448888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232326464646464646464646464646464
order12442224442222224444442222224444448888222222244444444444444444444444888888888888888888888844448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ81111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111111111111111-1-11-1-11111111-111-1-111-111-1-1111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ1011111111111111111111111111-1-11-1-11111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111
χ1111111111111111111111111111-1-11-1-11111111-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111111111111-1-11-1-11111111-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ1311111111111111111111111111-1-11-1-1111-1-1-1-1-111-1-111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ1411111111111111111111111111-1-11-1-1111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1
χ1511111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1
χ1611111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-111
χ1722222222222222-2-22222-2-22-2-2-200-2002-2-2222202-2000002-200000000000022-2-20000220000-2-2-2-200000000000000002-200000000
χ1822222222222222-2-22222-2-22-2-2-200-2002-2-222220-2200000-22000000000000-2-2220000220000-2-2-2-20000000000000000-2200000000
χ1922222222222222-2-22222-2-22-2-2-200-2002-2-2-2-2-2-202-2000002-200000000000022-2-20000-2-2000022220000000000000000-2200000000
χ2022222222222222-2-22222-2-22-2-2-200-2002-2-2-2-2-2-20-2200000-22000000000000-2-2220000-2-20000222200000000000000002-200000000
χ21222222222222-2-22222-2-222-22-2-222-222-22-20000200002-2200002-222-2-2-2-2-2-20000000000000000000000000000002-2000000000000
χ22222222222222-2-22222-2-222-22-2-222-222-22-2000020000-2220000-22-2-222-2-2-2-2000000000000000000000000000000-22000000000000
χ23222222222222-2-22222-2-222-22-2-2-2-2-2-2-2-22-20000-200002-2-200002-222-2-22222000000000000000000000000000000-22000000000000
χ24222222222222-2-22222-2-222-22-2-2-2-2-2-2-2-22-20000-20000-22-20000-22-2-22222220000000000000000000000000000002-2000000000000
χ252222222222-2-22222-2-22222-2-22-200200-2-2-2000002200220220022-2-2-2-20000-2-2-2-2000000000000000000-2-222000000000000000000
χ262222222222-2-22222-2-22222-2-22-200200-2-2-2000002200-2-202200-2-222220000-2-2-2-200000000000000000022-2-2000000000000000000
χ272222222222-2-22222-2-22222-2-22-200200-2-2-200000-2-200220-2-20022-2-2-2-20000222200000000000000000022-2-2000000000000000000
χ282222222222-2-22222-2-22222-2-22-200200-2-2-200000-2-200-2-20-2-200-2-2222200002222000000000000000000-2-222000000000000000000
χ292222222222-2-222-2-2-2-222-2-2-22-2200-200-222000002-2000002-2000000000000-2-22200000022220000-2-2-2-200000000002-20000000000
χ302222222222-2-222-2-2-2-222-2-2-22-2200-200-222000002-2000002-2000000000000-2-222000000-2-2-2-2000022220000000000-220000000000
χ312222222222-2-222-2-2-2-222-2-2-22-2200-200-22200000-2200000-2200000000000022-2-200000022220000-2-2-2-20000000000-220000000000
χ322222222222-2-222-2-2-2-222-2-2-22-2200-200-22200000-2200000-2200000000000022-2-2000000-2-2-2-20000222200000000002-20000000000
χ332222222222-2-2-2-222-2-2-2-2222-2-2200-2002-220000000222-2000222-2-2-22200000000-2-2-2-200000000000000000000000000002-2000000
χ342222222222-2-2-2-222-2-2-2-2222-2-2200-2002-22000000022-2200022-2222-2-200000000-2-2-2-20000000000000000000000000000-22000000
χ352222222222-2-2-2-222-2-2-2-2222-2-2200-2002-220000000-2-22-2000-2-22-2-2-2220000000022220000000000000000000000000000-22000000
χ362222222222-2-2-2-222-2-2-2-2222-2-2200-2002-220000000-2-2-22000-2-2-2222-2-200000000222200000000000000000000000000002-2000000
χ3722-2-2222-2-2-2222222-2-2-2-2-2-222-2-2222-2-2-2-222i2i−2i−2i2000000-2000000000022-2-2000000002i−2i00002i2i−2i−2i000000002i2i−2i−2i00000000000000
χ3822-2-2222-2-2-2222222-2-2-2-2-2-222-2-2222-2-2-2-22−2i−2i2i2i2000000-2000000000022-2-200000000−2i2i0000−2i−2i2i2i00000000−2i−2i2i2i00000000000000
χ3922-2-2222-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-2-222i2i−2i−2i-200000020000000000-2-222000000002i−2i00002i2i−2i−2i00000000−2i−2i2i2i00000000000000
χ4022-2-2222-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-2-22−2i−2i2i2i-200000020000000000-2-22200000000−2i2i0000−2i−2i2i2i000000002i2i−2i−2i00000000000000
χ4122-2-2222-2-2-22222-2-2-2-2-2-2222-22200-200-22-22i2i−2i−2i0002-2000002-20000000000000022-2-22i−2i0000−2i−2i2i2i000000000000000000002i−2i0000
χ4222-2-2222-2-2-22222-2-2-2-2-2-2222-22200-200-22-22i2i−2i−2i000-2200000-2200000000000000-2-2222i−2i0000−2i−2i2i2i00000000000000000000−2i2i0000
χ4322-2-2222-2-2-22222-2-2-2-2-2-2222-22200-200-22-2−2i−2i2i2i0002-2000002-20000000000000022-2-2−2i2i00002i2i−2i−2i00000000000000000000−2i2i0000
χ4422-2-2222-2-2-22222-2-2-2-2-2-2222-22200-200-22-2−2i−2i2i2i000-2200000-2200000000000000-2-222−2i2i00002i2i−2i−2i000000000000000000002i−2i0000
χ4522-2-2222-2-2-222-2-222-2-222-2-2-222222-2-2-22-2-200002000000-20000000000-2-22200000000002i2i−2i−2i00002i2i−2i−2i0000000000000000002i−2i00
χ4622-2-2222-2-2-222-2-222-2-222-2-2-222222-2-2-22-2-200002000000-20000000000-2-2220000000000−2i−2i2i2i0000−2i−2i2i2i000000000000000000−2i2i00
χ4722-2-2222-2-2-222-2-222-2-222-2-2-2222-2-2-2222-2-20000-20000002000000000022-2-200000000002i2i−2i−2i00002i2i−2i−2i000000000000000000−2i2i00
χ4822-2-2222-2-2-222-2-222-2-222-2-2-2222-2-2-2222-2-20000-20000002000000000022-2-20000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000002i−2i00
χ4922-2-2222-2-2-2-2-2-2-2-2-222222222-2200200-2-2-200000002-2000002-200000000000000-2-222002i2i−2i−2i0000−2i−2i2i2i000000000000000000002i−2i
χ5022-2-2222-2-2-2-2-2-2-2-2-222222222-2200200-2-2-200000002-2000002-200000000000000-2-22200−2i−2i2i2i00002i2i−2i−2i00000000000000000000−2i2i
χ5122-2-2222-2-2-2-2-2-2-2-2-222222222-2200200-2-2-20000000-2200000-220000000000000022-2-2002i2i−2i−2i0000−2i−2i2i2i00000000000000000000−2i2i
χ5222-2-2222-2-2-2-2-2-2-2-2-222222222-2200200-2-2-20000000-2200000-220000000000000022-2-200−2i−2i2i2i00002i2i−2i−2i000000000000000000002i−2i
χ53444444444444-4-4-4-444-4-4-4-4-4-44400400-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-4-4-4-4-4444-40040044-40000000000000000000000000000000000000000000000000000000000000000000000
χ554444-44-4-4-4400004-400004-4000000000000222200000000000000004-4000000000000-2-22-22-22-22-22-22-20000000000000000000000
χ564444-44-4-4-4400004-400004-400000000000022220000000000000000-44000000000000-2-2-22-222-22-2-22-220000000000000000000000
χ574444-44-4-4-4400004-400004-4000000000000-2-2-2-200000000000000004-400000000000022-22-22-22-22-22-220000000000000000000000
χ584444-44-4-4-4400004-400004-4000000000000-2-2-2-20000000000000000-44000000000000222-22-2-22-222-22-20000000000000000000000
χ594444-44-4-4-440000-440000-440000000000002222000000000000004-400000000000000-2-22-22-2-22-22-22-220000000000000000000000
χ604444-44-4-4-440000-440000-44000000000000222200000000000000-4400000000000000-2-2-22-22-22-222-22-20000000000000000000000
χ614444-44-4-4-440000-440000-44000000000000-2-2-2-2000000000000004-40000000000000022-22-222-22-22-22-20000000000000000000000
χ624444-44-4-4-440000-440000-44000000000000-2-2-2-200000000000000-4400000000000000222-22-22-22-2-22-220000000000000000000000
χ634444-4-444-4-4004-400004-4000000220220000000-2002-200-200-220000002-22-2004-42-22-2000000000000000000000000000000000000
χ644444-4-444-4-4004-400004-4000000220220000000-200-2200-2002-20000002-22-200-44-22-22000000000000000000000000000000000000
χ654444-4-444-4-4004-400004-4000000-2-20-2-200000002002-200200-22000000-22-2200-442-22-2000000000000000000000000000000000000
χ664444-4-444-4-4004-400004-4000000-2-20-2-20000000200-22002002-2000000-22-22004-4-22-22000000000000000000000000000000000000
χ674444-4-444-4-400-440000-44000000220220000000-2002-200-200-22000000-22-224-400-22-22000000000000000000000000000000000000
χ684444-4-444-4-400-440000-44000000220220000000-200-2200-2002-2000000-22-22-44002-22-2000000000000000000000000000000000000
χ694444-4-444-4-400-440000-44000000-2-20-2-200000002002-200200-220000002-22-2-4400-22-22000000000000000000000000000000000000
χ704444-4-444-4-400-440000-44000000-2-20-2-20000000200-22002002-20000002-22-24-4002-22-2000000000000000000000000000000000000
χ7144-4-4444-4-4-444-4-4-4-4-4-44444-4-4-4-4004004440000000000000000000000000000000000000000000000000000000000000000000000
χ7244-4-4444-4-4-4-4-4444444-4-4-4-4-4-4-440040044-40000000000000000000000000000000000000000000000000000000000000000000000
χ7344-4-4444-4-4-4-4-444-4-444-4-444-444-400-4004-440000000000000000000000000000000000000000000000000000000000000000000000
χ7444-4-4444-4-4-4-4-4-4-4444444-4-44-44-400-400-4440000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-444-400004-40000-440000000000002i2i−2i−2i0000004000000-40000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ7644-4-4-44-444-400004-40000-440000000000002i2i−2i−2i000000-400000040000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ7744-4-4-44-444-400004-40000-44000000000000−2i−2i2i2i0000004000000-400000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ7844-4-4-44-444-400004-40000-44000000000000−2i−2i2i2i000000-4000000400000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ7944-4-4-44-444-40000-4400004-40000000000002i2i−2i−2i000004000000-400000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ8044-4-4-44-444-40000-4400004-40000000000002i2i−2i−2i00000-4000000400000000000000000−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ8144-4-4-44-444-40000-4400004-4000000000000−2i−2i2i2i000004000000-4000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ8244-4-4-44-444-40000-4400004-4000000000000−2i−2i2i2i00000-40000004000000000000000002i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ8344-4-4-4-44-444004-40000-44000000220-2-20000000-204220020-4-2-20000002-2-2200002-2-22000000000000000000000000000000000000
χ8444-4-4-4-44-444004-40000-44000000220-2-20000000-20-4-2-200204220000002-2-220000-222-2000000000000000000000000000000000000
χ8544-4-4-4-44-444004-40000-44000000-2-20220000000204-2-200-20-422000000-222-20000-222-2000000000000000000000000000000000000
χ8644-4-4-4-44-444004-40000-44000000-2-2022000000020-42200-204-2-2000000-222-200002-2-22000000000000000000000000000000000000
χ8744-4-4-4-44-44400-4400004-4000000220-2-20000000-24022002-40-2-2000000-222-20000-222-2000000000000000000000000000000000000
χ8844-4-4-4-44-44400-4400004-4000000220-2-20000000-2-40-2-20024022000000-222-200002-2-22000000000000000000000000000000000000
χ8944-4-4-4-44-44400-4400004-4000000-2-20220000000240-2-200-2-40220000002-2-2200002-2-22000000000000000000000000000000000000
χ9044-4-4-4-44-44400-4400004-4000000-2-202200000002-402200-240-2-20000002-2-220000-222-2000000000000000000000000000000000000
χ9188888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000004-4000000000000000000
χ9288888-8-8-88-800000000000000000000000000000000000000000000000000000000000000000000000000-44000000000000000000
χ9388-8-88-8-88-880000000000000000000000000000000000000000000000000000000000000000000000004i−4i00000000000000000000
χ9488-8-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000−4i4i00000000000000000000
χ958-88i−8i0000004-400004i−4i000000004-404i−4i0004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ968-88i−8i0000004-400004i−4i000000004-404i−4i000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ978-88i−8i0000004-400004i−4i00000000-440−4i4i0004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ988-88i−8i0000004-400004i−4i00000000-440−4i4i000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ998-8−8i8i0000004-40000−4i4i000000004-40−4i4i0004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ1008-8−8i8i0000004-40000−4i4i000000004-40−4i4i000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ1018-8−8i8i0000004-40000−4i4i00000000-4404i−4i0004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ1028-8−8i8i0000004-40000−4i4i00000000-4404i−4i000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ10316-1616i−16i000000-880000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10416-16−16i16i000000-8800008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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