Finite Group Databasebeta

← Group #357751

Character table — Group #357751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12224444222222444444444444442244444444444444888888882222444422222244444444444444224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−i
χ1011-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111-1-111−i−iii11-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111-1-111−i−iii
χ1111-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1-1-111−i−iii11-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1-1-111−i−iii
χ1211-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11−i−iii−i−iii-1-11111-1-1ii−i−i11-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11−i−iii−i−iii-1-11111-1-1ii−i−i
χ1311-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111-1-111ii−i−i11-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111-1-111ii−i−i
χ1411-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii
χ1511-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11ii−i−iii−i−i-1-11111-1-1−i−iii11-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11ii−i−iii−i−i-1-11111-1-1−i−iii
χ1611-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1-1-111ii−i−i11-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1-1-111ii−i−i
χ17222222222-22-2-2-22-2-2-2-2200000000000000000000000000002-22-2222222222-22-2-2-22-2-2-2-2200000000000000000000000000002-22-2
χ18222222222-22-2-2-22-2-2-2-220000000000000000000000000000-22-22222222222-22-2-2-22-2-2-2-220000000000000000000000000000-22-22
χ1922222222-22-2-2-22-22-22-2-200000000000000002-22-200000000000022222222-22-2-2-22-22-22-2-200000000000000002-22-2000000000000
χ2022222222-22-2-2-22-22-22-2-20000000000000000-22-2200000000000022222222-22-2-2-22-22-22-2-20000000000000000-22-22000000000000
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χ2222222222-2-2-222-2-2-22-22-200000000000000000000-22-220000000022222222-2-2-222-2-2-22-22-200000000000000000000-22-2200000000
χ232222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-20000000000000000000000002222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-2000000000000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000002222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ252222-2-2-2-22-22-2-2-2-22222-20000000000000000000000002i−2i2i−2i00002222-2-2-2-22-22-2-2-2-22222-20000000000000000000000002i−2i2i−2i0000
χ262222-2-2-2-22-22-2-2-2-22222-2000000000000000000000000−2i2i−2i2i00002222-2-2-2-22-22-2-2-2-22222-2000000000000000000000000−2i2i−2i2i0000
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χ282222-2-2-2-2-22-2-2-222-22-22200000000-2-222000000000000000000002222-2-2-2-2-22-2-2-222-22-22200000000-2-22200000000000000000000
χ292222-2-2-2-2-2-2-222-222-22-220000000000002-22-200000000000000002222-2-2-2-2-2-2-222-222-22-220000000000002-22-20000000000000000
χ302222-2-2-2-2-2-2-222-222-22-22000000000000-22-2200000000000000002222-2-2-2-2-2-2-222-222-22-22000000000000-22-220000000000000000
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χ3522-2-222-2-2-2222-2-22-222-2-2000000002-2-220000000000000000000022-2-222-2-2-2222-2-22-222-2-2000000002-2-2200000000000000000000
χ3622-2-222-2-2-2222-2-22-222-2-200000000-222-20000000000000000000022-2-222-2-2-2222-2-22-222-2-200000000-222-200000000000000000000
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χ4022-2-2-2-2222-2-22-222-2-222-20000000000000000000000000000−2i2i2i−2i22-2-2-2-2222-2-22-222-2-222-20000000000000000000000000000−2i2i2i−2i
χ4122-2-2-2-222-2222-2-2-22-2-22200000000000000002i−2i−2i2i00000000000022-2-2-2-222-2222-2-2-22-2-22200000000000000002i−2i−2i2i000000000000
χ4222-2-2-2-222-2222-2-2-22-2-2220000000000000000−2i2i2i−2i00000000000022-2-2-2-222-2222-2-2-22-2-2220000000000000000−2i2i2i−2i000000000000
χ4322-2-2-2-222-2-22-222-2-222-22000000000000000000002-2-220000000022-2-2-2-222-2-22-222-2-222-22000000000000000000002-2-2200000000
χ4422-2-2-2-222-2-22-222-2-222-2200000000000000000000-222-20000000022-2-2-2-222-2-22-222-2-222-2200000000000000000000-222-200000000
χ454-44-44i−4i4i−4i0000000000002-22i−2i2-22i−2i0000000000000000000000004-44-44i−4i4i−4i0000000000002-22i−2i2-22i−2i000000000000000000000000
χ464-44-44i−4i4i−4i000000000000-22−2i2i-22−2i2i0000000000000000000000004-44-44i−4i4i−4i000000000000-22−2i2i-22−2i2i000000000000000000000000
χ474-44-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i0000000000000000000000004-44-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ484-44-4−4i4i−4i4i000000000000-222i−2i-222i−2i0000000000000000000000004-44-4−4i4i−4i4i000000000000-222i−2i-222i−2i000000000000000000000000
χ494-4-444i−4i−4i4i0000000000002i−2i2-2−2i2i-220000000000000000000000004-4-444i−4i−4i4i0000000000002i−2i2-2−2i2i-22000000000000000000000000
χ504-4-444i−4i−4i4i000000000000−2i2i-222i−2i2-20000000000000000000000004-4-444i−4i−4i4i000000000000−2i2i-222i−2i2-2000000000000000000000000
χ514-4-44−4i4i4i−4i0000000000002i−2i-22−2i2i2-20000000000000000000000004-4-44−4i4i4i−4i0000000000002i−2i-22−2i2i2-2000000000000000000000000
χ524-4-44−4i4i4i−4i000000000000−2i2i2-22i−2i-220000000000000000000000004-4-44−4i4i4i−4i000000000000−2i2i2-22i−2i-22000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ551111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111
χ561111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ5711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ5811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ6011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
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χ6211-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111-1-111−i−iii-1-11111-1-1-1-111-11-1-1-1111−i−i−i−iiiii-11-11ii−i−i−i−iii11-1-111-1-1ii−i−i
χ6311-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1-1-111−i−iii-1-11111-1-1-1-111-11-1-1-1111−i−i−i−iiiii1-11-1−i−iiiii−i−i-1-11111-1-1ii−i−i
χ6411-1-1-1-11111-1-11-1111-1-1-1iiii−i−i−i−i-11-11−i−iii−i−iii-1-11111-1-1ii−i−i-1-11111-1-1-1-111-11-1-1-1111−i−i−i−iiiii1-11-1ii−i−iii−i−i11-1-1-1-111−i−iii
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χ6611-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii-1-11111-1-1-1-111-11-1-1-1111iiii−i−i−i−i-11-11ii−i−iii−i−i-1-111-1-111ii−i−i
χ6711-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11ii−i−iii−i−i-1-11111-1-1−i−iii-1-11111-1-1-1-111-11-1-1-1111iiii−i−i−i−i1-11-1−i−iii−i−iii11-1-1-1-111ii−i−i
χ6811-1-1-1-11111-1-11-1111-1-1-1−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1-1-111ii−i−i-1-11111-1-1-1-111-11-1-1-1111iiii−i−i−i−i1-11-1ii−i−i−i−iii-1-11111-1-1−i−iii
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χ9522-2-2-2-222-2-22-222-2-222-22000000000000000000002-2-2200000000-2-22222-2-222-22-2-222-2-22-200000000000000000000-222-200000000
χ9622-2-2-2-222-2-22-222-2-222-2200000000000000000000-222-200000000-2-22222-2-222-22-2-222-2-22-2000000000000000000002-2-2200000000
χ974-44-44i−4i4i−4i0000000000002-22i−2i2-22i−2i000000000000000000000000-44-44−4i4i−4i4i000000000000-22−2i2i-22−2i2i000000000000000000000000
χ984-44-44i−4i4i−4i000000000000-22−2i2i-22−2i2i000000000000000000000000-44-44−4i4i−4i4i0000000000002-22i−2i2-22i−2i000000000000000000000000
χ994-44-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000-44-444i−4i4i−4i000000000000-222i−2i-222i−2i000000000000000000000000
χ1004-44-4−4i4i−4i4i000000000000-222i−2i-222i−2i000000000000000000000000-44-444i−4i4i−4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ1014-4-444i−4i−4i4i0000000000002i−2i2-2−2i2i-22000000000000000000000000-444-4−4i4i4i−4i000000000000−2i2i-222i−2i2-2000000000000000000000000
χ1024-4-444i−4i−4i4i000000000000−2i2i-222i−2i2-2000000000000000000000000-444-4−4i4i4i−4i0000000000002i−2i2-2−2i2i-22000000000000000000000000
χ1034-4-44−4i4i4i−4i0000000000002i−2i-22−2i2i2-2000000000000000000000000-444-44i−4i−4i4i000000000000−2i2i2-22i−2i-22000000000000000000000000
χ1044-4-44−4i4i4i−4i000000000000−2i2i2-22i−2i-22000000000000000000000000-444-44i−4i−4i4i0000000000002i−2i-22−2i2i2-2000000000000000000000000

Here i is the imaginary unit (i² = −1).