Finite Group Databasebeta

← Group #72286252

Character table — Group #72286252

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11222444444444444448888888888888888161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323232323232323264646464
order122442224444488888844488888161616161616161688888888161616162224444488888888161616161616161616161616323232323232323232323232323232324488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ911111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1iiii−i−i−i−i11-1-111-1-111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1
χ1011111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1iiii−i−i−i−i11-1-111-1-111-1-1iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111
χ1111111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1iiii−i−i−i−i11-1-1-1-111-1-111−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1
χ1211111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1iiii−i−i−i−i11-1-1-1-111-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111
χ1311111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1−i−i−i−iiiii11-1-111-1-111-1-1−i−i−i−iiiii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111
χ1411111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1−i−i−i−iiiii11-1-111-1-111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1
χ1511111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1−i−i−i−iiiii11-1-1-1-111-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111
χ1611111111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1−i−i−i−iiiii11-1-1-1-111-1-111iiii−i−i−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1
χ1711111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11-11-11-11-11-11-111-1-111-1-11-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-1
χ1811111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11-11-11-11-11-11-111-1-111-1-11-11-1-1-111-1-111-1-111-1-111-1-111-1-111-11-11
χ1911111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-11-11-11-11-1-111-1-1111-11-111-1-111-1-1-1-111-1-111-1-111-1-1111-11-1
χ2011111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-11-11-11-11-1-111-1-1111-11-1-1-111-1-11111-1-111-1-111-1-111-1-1-11-11
χ2111111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-11-11-11-11-11-1-1-111-1-111-11-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-11
χ2211111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-11-11-11-11-11-1-1-111-1-111-11-11-1-111-1-111-1-111-1-11111-1-111-1-11-11-1
χ2311111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1-11-11-11-1111-1-111-1-1-11-1111-1-111-1-1-1-111-1-11111-1-111-1-1-11-11
χ2411111-1-11-1-11111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1-11-11-11-1111-1-111-1-1-11-11-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1
χ2511111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iii1-1-111-1-111-1-11ii−i−i−i−iiii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-1111-1-11
χ2611111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iii1-1-111-1-111-1-11ii−i−i−i−iiii−i−ii−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-111-1
χ2711111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iii1-1-11-111-1-111-1−i−iiiii−i−ii−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-11-1-11
χ2811111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iii1-1-11-111-1-111-1−i−iiiii−i−ii−i−ii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-111-1
χ2911111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i1-1-111-1-111-1-11−i−iiiii−i−i−iii−iii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-111-1
χ3011111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i1-1-111-1-111-1-11−i−iiiii−i−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-1111-1-11
χ3111111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i1-1-11-111-1-111-1ii−i−i−i−iii−iii−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-111-1
χ3211111-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i1-1-11-111-1-111-1ii−i−i−i−iii−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-11-1-11
χ33222222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-2-2-20000000000000000000000000000
χ34222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000000000
χ3522222222222-2-2-2-222-2-2-2-2-2222-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i-2-2220000000000000000−2i−2i2i2i0000000000000000000000000000
χ3622222222222-2-2-2-222-2-2-2-2-2222-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i-2-22200000000000000002i2i−2i−2i0000000000000000000000000000
χ37222222-2-22-2-22222-2-2-2-2-22-222-22-2000000002-22-22-22-200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000
χ38222222-2-22-2-22222-2-2-2-2-22-222-22-2000000002-22-22-22-200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000
χ39222222-2-22-2-22222-2-2-2-2-22-222-22-200000000-22-22-22-2200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000
χ40222222-2-22-2-22222-2-2-2-2-22-222-22-200000000-22-22-22-2200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000
χ41222222-2-22-2-222-2-22222-22-2-2-22-22222222-2-200000000-2-22-2000000002-22-22-22-200000000000000000000000000000000
χ42222222-2-22-2-222-2-22222-22-2-2-22-22222222-2-200000000-2-22-200000000-22-22-22-2200000000000000000000000000000000
χ43222222-2-22-2-222-2-22222-22-2-2-22-22-2-2-2-2-2-2220000000022-222-2-22-222-20000000000000000000000000000000000000000
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χ46222222-2-22-2-2-2-22222-2-22-22-2-222-222-2-2222200000000-2-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ47222222-2-22-2-2-2-22222-2-22-22-2-222-2-2-222-2-2-2-200000000222-22-22-2-22-220000000000000000000000000000000000000000
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χ50222222-2-22-2-2-2-2-2-2-2-2222-2222-2-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000
χ51222222-2-22-2-2-2-2-2-2-2-2222-2222-2-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000
χ52222222-2-22-2-2-2-2-2-2-2-2222-2222-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000
χ5322222-22-2-22-22222-2-2-2-2-2-222-22-22000000002-2-222-2-2200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000
χ5422222-22-2-22-22222-2-2-2-2-2-222-22-22000000002-2-222-2-2200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000
χ5522222-22-2-22-22222-2-2-2-2-2-222-22-2200000000-222-2-222-200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000
χ5622222-22-2-22-22222-2-2-2-2-2-222-22-2200000000-222-2-222-200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000
χ5722222-22-2-22-222-2-22222-2-22-22-22-22222-2-222000000002-2-2-222-2-2-2-2220000000000000000000000000000000000000000
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χ6522222-22-2-22-2-2-2-2-2-2-22222-22-222-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000
χ6622222-22-2-22-2-2-2-2-2-2-22222-22-222-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i20000
χ6722222-22-2-22-2-2-2-2-2-2-22222-22-222-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000
χ6822222-22-2-22-2-2-2-2-2-2-22222-22-222-200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000
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χ7222222-2-22-2-22-2-2-2-222-2-2-2222-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i-222-200000000000000002i−2i−2i2i0000000000000000000000000000
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χ9532-32000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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