Finite Group Databasebeta

← Group #72266593

Character table — Group #72266593

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111114444444444444444888888161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232
order12222222444444442222222244444444222444222222444444444444444444444444444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1011111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ1111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1211111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ1311111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1411111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ1511111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111
χ1611111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
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χ3922222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-22-22-2200-2-200002200002-200000022-2-200000000-2-2220000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-22-22-2200-2-200002200002-2000000-2-2220000000022-2-20000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222-2-222-20000220000-2-20000-220000000022-2-20000000022-2-2000000000000000000000000
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χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222-2-222-20000-2-200002200002-20000000022-2-200000000-2-222000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222-2-222-20000-2-200002200002-200000000-2-2220000000022-2-2000000000000000000000000
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χ584444-4-4-4-4−4i−4i−4i−4i4i4i4i4i0000004-4−4i4i0000000000000000000000000000002-2−2i2i-222i−2i-222i−2i000000000000000000000000000000000000
χ594444-4-4-4-4−4i−4i−4i−4i4i4i4i4i0000004-4−4i4i000000000000000000000000000000-222i−2i2-2−2i2i-222i−2i000000000000000000000000000000000000
χ604444-4-4-4-4−4i−4i−4i−4i4i4i4i4i0000004-4−4i4i000000000000000000000000000000-222i−2i-222i−2i2-2−2i2i000000000000000000000000000000000000
χ6144-4-444-4-44i4i−4i−4i4i4i−4i−4i00004-400004i−4i0000000000000000000000000000000000000000000000002i−2i2-22ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3000000000000
χ6244-4-444-4-44i4i−4i−4i4i4i−4i−4i00004-400004i−4i0000000000000000000000000000000000000000000000002i−2i2-2−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3000000000000
χ6344-4-444-4-44i4i−4i−4i4i4i−4i−4i00004-400004i−4i000000000000000000000000000000000000000000000000−2i2i-222ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ3000000000000
χ6444-4-444-4-44i4i−4i−4i4i4i−4i−4i00004-400004i−4i000000000000000000000000000000000000000000000000−2i2i-22−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ3000000000000
χ6544-4-444-4-4−4i−4i4i4i−4i−4i4i4i00004-40000−4i4i0000000000000000000000000000000000000000000000002i−2i-222ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ000000000000
χ6644-4-444-4-4−4i−4i4i4i−4i−4i4i4i00004-40000−4i4i0000000000000000000000000000000000000000000000002i−2i-22−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ000000000000
χ6744-4-444-4-4−4i−4i4i4i−4i−4i4i4i00004-40000−4i4i000000000000000000000000000000000000000000000000−2i2i2-22ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ000000000000
χ6844-4-444-4-4−4i−4i4i4i−4i−4i4i4i00004-40000−4i4i000000000000000000000000000000000000000000000000−2i2i2-2−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ000000000000
χ694-44-44-44-44i−4i4i−4i4i−4i4i−4i004-4000000004i−4i0000000000000000000000000000000000000000002i−2i2-2000000002ζ−2ζ2ζ3−2ζ3000000002ζ−2ζ2ζ3−2ζ30000
χ704-44-44-44-44i−4i4i−4i4i−4i4i−4i004-4000000004i−4i0000000000000000000000000000000000000000002i−2i2-200000000−2ζ2ζ−2ζ32ζ300000000−2ζ2ζ−2ζ32ζ30000
χ714-44-44-44-44i−4i4i−4i4i−4i4i−4i004-4000000004i−4i000000000000000000000000000000000000000000−2i2i-22000000002ζ−2ζ2ζ3−2ζ300000000−2ζ2ζ−2ζ32ζ30000
χ724-44-44-44-44i−4i4i−4i4i−4i4i−4i004-4000000004i−4i000000000000000000000000000000000000000000−2i2i-2200000000−2ζ2ζ−2ζ32ζ3000000002ζ−2ζ2ζ3−2ζ30000
χ734-44-44-44-4−4i4i−4i4i−4i4i−4i4i004-400000000−4i4i0000000000000000000000000000000000000000002i−2i-22000000002ζ3−2ζ32ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ0000
χ744-44-44-44-4−4i4i−4i4i−4i4i−4i4i004-400000000−4i4i0000000000000000000000000000000000000000002i−2i-2200000000−2ζ32ζ3−2ζ2ζ000000002ζ3−2ζ32ζ−2ζ0000
χ754-44-44-44-4−4i4i−4i4i−4i4i−4i4i004-400000000−4i4i000000000000000000000000000000000000000000−2i2i2-2000000002ζ3−2ζ32ζ−2ζ000000002ζ3−2ζ32ζ−2ζ0000
χ764-44-44-44-4−4i4i−4i4i−4i4i−4i4i004-400000000−4i4i000000000000000000000000000000000000000000−2i2i2-200000000−2ζ32ζ3−2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ0000
χ774-4-44-444-44i−4i−4i4i−4i4i4i−4i4-40000000000004i−4i0000000000000000000000000000000000002i−2i2-2000000000000000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3
χ784-4-44-444-44i−4i−4i4i−4i4i4i−4i4-40000000000004i−4i0000000000000000000000000000000000002i−2i2-200000000000000000000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3
χ794-4-44-444-44i−4i−4i4i−4i4i4i−4i4-40000000000004i−4i000000000000000000000000000000000000−2i2i-22000000000000000000002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ3
χ804-4-44-444-44i−4i−4i4i−4i4i4i−4i4-40000000000004i−4i000000000000000000000000000000000000−2i2i-2200000000000000000000−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ3
χ814-4-44-444-4−4i4i4i−4i4i−4i−4i4i4-4000000000000−4i4i0000000000000000000000000000000000002i−2i-22000000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ
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χ834-4-44-444-4−4i4i4i−4i4i−4i−4i4i4-4000000000000−4i4i000000000000000000000000000000000000−2i2i2-2000000000000000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ
χ844-4-44-444-4−4i4i4i−4i4i−4i−4i4i4-4000000000000−4i4i000000000000000000000000000000000000−2i2i2-200000000000000000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ
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χ938-88-88-88-88i−8i8i−8i8i−8i8i−8i00-8800000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000
χ948-88-88-88-8−8i8i−8i8i−8i8i−8i8i00-88000000008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000
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χ1028-8-888-8-88-888-8-888-80000000000000000000000-4400004-40000000000000000000000000000000000000000000000000000000000
χ1038-8-88-888-88i−8i−8i8i−8i8i8i−8i-88000000000000−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-888-8−8i8i8i−8i8i−8i−8i8i-880000000000008i−8i000000000000000000000000000000000000000000000000000000000000000000000000

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