Finite Group Databasebeta

← Group #122016

Character table — Group #122016

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444448888888888888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1
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χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11
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χ202222222222222222-2-2-2-2-2-2-2-222-2-22-22-20000000000000000000000000000000000000000-2-2002200
χ212222222222222222-2-2-2-2-2-2-2-2-2-222-22-220000000000000000000000000000000000000000002200-2-2
χ222222222222222222-2-2-2-2-2-2-2-2-2-222-22-22000000000000000000000000000000000000000000-2-20022
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-22-2200000000000000000000000000000000000000002-200-2200
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-22-220000000000000000000000000000000000000000-22002-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222-22-20000000000000000000000000000000000000000002-200-22
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222-22-2000000000000000000000000000000000000000000-22002-2
χ292222-2-2-2-22222-2-2-2-222-2-222-2-22-22-22-2-220000000000000000000000000000000022-2-222-2-200000000
χ302222-2-2-2-22222-2-2-2-222-2-222-2-22-22-22-2-2200000000000000000000000000000000-2-222-2-22200000000
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χ342222-2-2-2-22222-2-2-2-2-2-222-2-2222-2-2222-2-20000000000000000-2-222-2-222000000000000000000000000
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χ442222-2-2-2-2-2-2-2-22222-2-22222-2-2-222-222-2-200000000-2-22222-2-200000000000000000000000000000000
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χ4722-2-22-22-22i2i−2i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000000000−2i2i00-2200000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
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χ5122-2-22-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000000000−2i2i002-200000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ5222-2-22-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000000000−2i2i002-20000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ5322-2-2-22-222i2i−2i−2i−2i2i−2i2i2-2-222i−2i−2i2i000000002i−2i002-20000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5422-2-2-22-222i2i−2i−2i−2i2i−2i2i2-2-222i−2i−2i2i000000002i−2i002-2000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
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χ5622-2-2-22-222i2i−2i−2i−2i2i−2i2i2-2-222i−2i−2i2i00000000−2i2i00-22000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5722-2-2-22-22−2i−2i2i2i2i−2i2i−2i2-2-22−2i2i2i−2i000000002i−2i00-220000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ5822-2-2-22-22−2i−2i2i2i2i−2i2i−2i2-2-22−2i2i2i−2i000000002i−2i00-22000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
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χ6144-4-44-44-44i4i−4i−4i4i−4i4i−4i-44-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6244-4-44-44-4−4i−4i4i4i−4i4i−4i4i-44-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i4i−4i−4i−4i4i−4i4i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44−4i−4i4i4i4i−4i4i−4i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ654-44-444-4-44-44-444-4-4000000000000000000000000000000002-22-22-22-2000000000000000000000000
χ664-44-444-4-44-44-444-4-400000000000000000000000000000000-22-22-22-22000000000000000000000000
χ674-44-444-4-4-44-44-4-444000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ684-44-444-4-4-44-44-4-44400000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ694-44-4-4-4444-44-4-4-444000000000000000000000000000000002-2-222-2-22000000000000000000000000
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χ714-44-4-4-444-44-4444-4-4000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ724-44-4-4-444-44-4444-4-400000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ734-4-444-4-444i−4i−4i4i4i−4i−4i4i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ744-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ754-4-444-4-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ764-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ774-4-44-444-44i−4i−4i4i−4i4i4i−4i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ784-4-44-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ794-4-44-444-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ804-4-44-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000

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