Finite Group Databasebeta

← Group #102124

Character table — Group #102124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444444444444444444448888888888888888888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000002222-2-2-2-22222-2-2-2-20000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-22222-2-2-2-222220000000000000000
χ192222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
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χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
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χ782-2-2-2-22222222-2-2-2-2000000002-22-2000000002-22-200002-2-2200002-2-22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ792-2-2-2-22222222-2-2-2-2000000002-22-2000000002-22-20000-222-20000-222-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ802-2-2-2-22222222-2-2-2-2000000002-22-2000000002-22-20000-222-20000-222-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ812-2-2-2-22222222-2-2-2-200000000-22-2200000000-22-222-2-2200002-2-220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ822-2-2-2-22222222-2-2-2-200000000-22-2200000000-22-222-2-2200002-2-220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ832-2-2-2-22222222-2-2-2-200000000-22-2200000000-22-22-222-20000-222-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ842-2-2-2-22222222-2-2-2-200000000-22-2200000000-22-22-222-20000-222-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ852-2-2-2-2222-2-2-2-22222000000002-22-200000000-22-222-2-220000-222-200002−2−22−222−2−222−22−2−22−222−22−2−222−2−22−222−20000000000000000
χ862-2-2-2-2222-2-2-2-22222000000002-22-200000000-22-222-2-220000-222-20000−222−22−2−222−2−22−222−22−2−22−222−2−222−22−2−220000000000000000
χ872-2-2-2-2222-2-2-2-22222000000002-22-200000000-22-22-222-200002-2-2200002−2−22−222−2−222−22−2−222−2−22−222−2−222−22−2−220000000000000000
χ882-2-2-2-2222-2-2-2-22222000000002-22-200000000-22-22-222-200002-2-220000−222−22−2−222−2−22−222−2−222−22−2−222−2−22−222−20000000000000000
χ892-2-2-2-2222-2-2-2-2222200000000-22-22000000002-22-200002-2-220000-222-22−2−222−2−22−222−2−222−2−222−2−222−22−2−222−2−220000000000000000
χ902-2-2-2-2222-2-2-2-2222200000000-22-22000000002-22-200002-2-220000-222-2−222−2−222−22−2−222−2−222−2−222−2−22−222−2−222−20000000000000000
χ912-2-2-2-2222-2-2-2-2222200000000-22-22000000002-22-20000-222-200002-2-222−2−222−2−22−222−2−222−22−2−222−2−22−222−2−222−20000000000000000
χ922-2-2-2-2222-2-2-2-2222200000000-22-22000000002-22-20000-222-200002-2-22−222−2−222−22−2−222−2−22−222−2−222−22−2−222−2−220000000000000000
χ9344-4-44-4-444i−4i−4i4i4i−4i−4i4i00004-4-44000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-444i−4i−4i4i4i−4i−4i4i0000-444-400000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44−4i4i4i−4i−4i4i4i−4i00004-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44−4i4i4i−4i−4i4i4i−4i0000-444-4000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-444i−4i−4i4i−4i4i4i−4i4-4-44000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-444i−4i−4i4i−4i4i4i−4i-444-400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-44−4i4i4i−4i4i−4i−4i4i4-4-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-44−4i4i4i−4i4i−4i−4i4i-444-4000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-44i−4i4i−4i−4i4i−4i4i000000004i−4i−4i4i000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-44i−4i4i−4i−4i4i−4i4i00000000−4i4i4i−4i00000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1034-44-44-44-4−4i4i−4i4i4i−4i4i−4i000000004i−4i−4i4i00000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1044-44-44-44-4−4i4i−4i4i4i−4i4i−4i00000000−4i4i4i−4i000000004-4-440000000000000000000000000000000000000000000000000000000000000000

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