Finite Group Databasebeta

← Group #99564

Character table — Group #99564

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444444444444444444444888888888888888888888888
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
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χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
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χ202222222222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000-22-220000
χ212222222222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000002-22-2
χ222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000-22-22
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
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000002i−2i−2i2i0000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i
χ2922-22-2-22-22i2i−2i−2i2i2i−2i−2i2-22-22i2i−2i−2i0000000000002i−2i2-200000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000
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χ3322-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i0000000000002i−2i-2200000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
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χ3522-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i000000000000−2i2i2-200000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000
χ3622-22-2-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i000000000000−2i2i2-20000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
χ372-222-2-2-222i2i−2i−2i−2i−2i2i2i2-2-222i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000
χ382-222-2-2-222i2i−2i−2i−2i−2i2i2i2-2-222i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000
χ392-222-2-2-222i2i−2i−2i−2i−2i2i2i2-2-222i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ402-222-2-2-222i2i−2i−2i−2i−2i2i2i2-2-222i−2i2i−2i-22-22−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ412-222-2-2-222i2i−2i−2i−2i−2i2i2i-222-2−2i2i−2i2i2-2-222i−2i−2i2i00000000000000002i2i−2i−2i22-2-2000000000000000000000000
χ422-222-2-2-222i2i−2i−2i−2i−2i2i2i-222-2−2i2i−2i2i2-2-222i−2i−2i2i0000000000000000−2i−2i2i2i-2-222000000000000000000000000
χ432-222-2-2-222i2i−2i−2i−2i−2i2i2i-222-2−2i2i−2i2i-222-2−2i2i2i−2i000000002i2i−2i−2i22-2-200000000000000000000000000000000
χ442-222-2-2-222i2i−2i−2i−2i−2i2i2i-222-2−2i2i−2i2i-222-2−2i2i2i−2i00000000−2i−2i2i2i-2-22200000000000000000000000000000000
χ452-222-2-2-22−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000
χ462-222-2-2-22−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000
χ472-222-2-2-22−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ482-222-2-2-22−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i−2i2i-22-222i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ492-222-2-2-22−2i−2i2i2i2i2i−2i−2i-222-22i−2i2i−2i2-2-22−2i2i2i−2i00000000000000002i2i−2i−2i-2-222000000000000000000000000
χ502-222-2-2-22−2i−2i2i2i2i2i−2i−2i-222-22i−2i2i−2i2-2-22−2i2i2i−2i0000000000000000−2i−2i2i2i22-2-2000000000000000000000000
χ512-222-2-2-22−2i−2i2i2i2i2i−2i−2i-222-22i−2i2i−2i-222-22i−2i−2i2i000000002i2i−2i−2i-2-22200000000000000000000000000000000
χ522-222-2-2-22−2i−2i2i2i2i2i−2i−2i-222-22i−2i2i−2i-222-22i−2i−2i2i00000000−2i−2i2i2i22-2-200000000000000000000000000000000
χ532-2-2222-2-22222-2-2-2-222-2-22-2-22000000002-22-2000000000000000000002−2−22−222−22−2−22−222−200000000
χ542-2-2222-2-22222-2-2-2-222-2-22-2-22000000002-22-200000000000000000000−222−22−2−22−222−22−2−2200000000
χ552-2-2222-2-22222-2-2-2-222-2-22-2-2200000000-22-22000000000000000000002−2−22−222−2−222−22−2−2200000000
χ562-2-2222-2-22222-2-2-2-222-2-22-2-2200000000-22-2200000000000000000000−222−22−2−222−2−22−222−200000000
χ572-2-2222-2-2-2-2-2-2222222-2-2-222-2000000002-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ582-2-2222-2-2-2-2-2-2222222-2-2-222-2000000002-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ592-2-2222-2-2-2-2-2-2222222-2-2-222-200000000-222-200000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ602-2-2222-2-2-2-2-2-2222222-2-2-222-200000000-222-200000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ61444-44-4-4-44-44-44-44-4000000000000000000000000000000002-22-22-22-2000000000000000000000000
χ62444-44-4-4-44-44-44-44-400000000000000000000000000000000-22-22-22-22000000000000000000000000
χ63444-44-4-4-4-44-44-44-44000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ64444-44-4-4-4-44-44-44-4400000000000000000000000000000000-22-222-22-2000000000000000000000000
χ6544-44-4-44-44i4i−4i−4i4i4i−4i−4i-44-44−4i−4i4i4i00000000000000000000000000000000000000000000000000000000
χ6644-44-4-44-4−4i−4i4i4i−4i−4i4i4i-44-444i4i−4i−4i00000000000000000000000000000000000000000000000000000000
χ6744-4-4-44-444i−4i−4i4i4i−4i−4i4i0000000000000000000000002i−2i2i−2i2-22-200000000000000000000000000000000
χ6844-4-4-44-444i−4i−4i4i4i−4i−4i4i000000000000000000000000−2i2i−2i2i-22-2200000000000000000000000000000000
χ6944-4-4-44-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000002i−2i2i−2i-22-2200000000000000000000000000000000
χ7044-4-4-44-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000−2i2i−2i2i2-22-200000000000000000000000000000000
χ714-44-4-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ724-44-4-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ734-44-4-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ744-44-4-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ754-4-4444-4-44444-4-4-4-4-4-444-444-400000000000000000000000000000000000000000000000000000000
χ764-4-4444-4-4-4-4-4-44444-4-4444-4-4400000000000000000000000000000000000000000000000000000000
χ774-4-4-44-4444-44-4-44-440000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ784-4-4-44-4444-44-4-44-44000000000000000000000000-222-2-222-200000000000000000000000000000000
χ794-4-4-44-444-44-444-44-40000000000000000000000002-2-22-222-200000000000000000000000000000000
χ804-4-4-44-444-44-444-44-4000000000000000000000000-222-22-2-2200000000000000000000000000000000

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