Finite Group Databasebeta

← Group #10826845

Character table — Group #10826845

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order122222344444444666666612121212121212122244444444444466661212121212121212121212121212121212121212222244666666661212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-11-1-111-1111-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-11-1
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11-11
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-11
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-11-1-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-11-111-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-11-1-1-1111-1-111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-111-1-11
χ1722222222222-2-2-2-2222222222222222-2-222-2-200000000-2-2-2-20000000000000000-2-2-2-22-2000022-2-2000022-2-20000000000000000
χ1822222222222-2-2-2-2222222222222222-2-2-2-22200000000-2-2-2-20000000000000000-2-2-2-2-220000-2-2220000-2-2220000000000000000
χ192222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-20000000022220000000000000000-2-2-2-2-220000-2-222000022-2-20000000000000000
χ202222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2220000000022220000000000000000-2-2-2-22-2000022-2-20000-2-2220000000000000000
χ21222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-122-2-2-2-2-1-1-1-11111-1-1-1-11111000000000000
χ23222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111111111000000000000
χ24222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-2-222221111-1-1-1-11111-1-1-1-1000000000000
χ25222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i311112-20000-1-111−i3−i3i3i3-1-111−i3−i3i3i3000000000000
χ26222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i311112-20000-1-111i3i3−i3−i3-1-111i3i3−i3−i3000000000000
χ27222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i31111-22000011-1-1i3i3−i3−i311-1-1i3i3−i3−i3000000000000
χ28222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i31111-22000011-1-1−i3−i3i3i311-1-1−i3−i3i3i3000000000000
χ29222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-222222222-2-2-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-1-2-222-2-21111-1-1-1-1-1-1-1-11111000000000000
χ30222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-1000000000000
χ31222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-2-2-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-122-2-222-1-1-1-111111111-1-1-1-1000000000000
χ32222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-2-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-111111111000000000000
χ33222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-22000011-1-1−i3−i3i3i3-1-111i3i3−i3−i3000000000000
χ34222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-22000011-1-1i3i3−i3−i3-1-111−i3−i3i3i3000000000000
χ35222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i311112-20000-1-111i3i3−i3−i311-1-1−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i311112-20000-1-111−i3−i3i3i311-1-1i3i3−i3−i3000000000000
χ372222-2-2222-2-222-2-222-2-2-2-222222-2-2-2-22-200000000000022-2-2000000000000000022-2-2000000000000000000000002002-20-20000
χ382222-2-2222-2-222-2-222-2-2-2-222222-2-2-2-22-200000000000022-2-2000000000000000022-2-200000000000000000000000-200-22020000
χ392222-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-2-22000000000000-2-2220000000000000000-2-2220000000000000000000000202-200-200000
χ402222-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-2-22000000000000-2-2220000000000000000-2-2220000000000000000000000-20-2200200000
χ412222-2-22-2-22222-2-222-2-2-2-22-2-2-2-22222-22000000000000-2-222000000000000000022-2-200000000000000000000000200-220-20000
χ422222-2-22-2-22222-2-222-2-2-2-22-2-2-2-22222-22000000000000-2-222000000000000000022-2-200000000000000000000000-2002-2020000
χ432222-2-22-2-222-2-22222-2-2-2-22-2-2-2-222222-200000000000022-2-20000000000000000-2-222000000000000000000000020-2200-200000
χ442222-2-22-2-222-2-22222-2-2-2-22-2-2-2-222222-200000000000022-2-20000000000000000-2-2220000000000000000000000-202-200200000
χ452-2-22-22200002-22-2-2-2-2-222200000000002-22-2000022-2-200000000000022-2-222-2-22-22-200002-2000000002-22-22-22-2000000000000
χ462-2-22-22200002-22-2-2-2-2-222200000000002-22-20000-2-222000000000000-2-222-2-2222-22-20000-22000000002-22-2-22-22000000000000
χ472-2-22-22200002-22-2-2-2-2-22220000000000-22-22000022-2-200000000000022-2-222-2-22-22-20000-2200000000-22-22-22-22000000000000
χ482-2-22-22200002-22-2-2-2-2-22220000000000-22-220000-2-222000000000000-2-222-2-2222-22-200002-200000000-22-222-22-2000000000000
χ492-2-22-2220000-22-22-2-2-2-222200000000002-2-2222-2-20000000022-2-222-2-200000000-22-22002-20000002-22-22-2-220000000000000000
χ502-2-22-2220000-22-22-2-2-2-222200000000002-2-22-2-22200000000-2-222-2-22200000000-22-2200-22000000-22-222-2-220000000000000000
χ512-2-22-2220000-22-22-2-2-2-22220000000000-222-222-2-20000000022-2-222-2-200000000-22-2200-22000000-22-22-222-20000000000000000
χ522-2-22-2220000-22-22-2-2-2-22220000000000-222-2-2-22200000000-2-222-2-22200000000-22-22002-20000002-22-2-222-20000000000000000
χ532-2-22-22-100002-22-21111-1-1-1−i3−i3i3i3−i3−i3i3i3002-22-2000022-2-2−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3-1-111-1-111-11-1100002-2−i3i3−i3i3−i3i3i3−i3-11-11-11-11000000000000
χ542-2-22-22-100002-22-21111-1-1-1−i3−i3i3i3−i3−i3i3i3002-22-20000-2-222−i3i3−i3i3i3i3−i3−i3−i3−i3i3i311-1-111-1-1-11-110000-22−i3i3−i3i3i3−i3−i3i3-11-111-11-1000000000000
χ552-2-22-22-100002-22-21111-1-1-1−i3−i3i3i3−i3−i3i3i300-22-22000022-2-2−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3-1-111-1-111-11-110000-22i3−i3i3−i3i3−i3−i3i31-11-11-11-1000000000000
χ562-2-22-22-100002-22-21111-1-1-1−i3−i3i3i3−i3−i3i3i300-22-220000-2-222−i3i3−i3i3i3i3−i3−i3−i3−i3i3i311-1-111-1-1-11-1100002-2i3−i3i3−i3−i3i3i3−i31-11-1-11-11000000000000
χ572-2-22-22-100002-22-21111-1-1-1i3i3−i3−i3i3i3−i3−i3002-22-2000022-2-2i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3-1-111-1-111-11-1100002-2i3−i3i3−i3i3−i3−i3i3-11-11-11-11000000000000
χ582-2-22-22-100002-22-21111-1-1-1i3i3−i3−i3i3i3−i3−i3002-22-20000-2-222i3−i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-111-1-1-11-110000-22i3−i3i3−i3−i3i3i3−i3-11-111-11-1000000000000
χ592-2-22-22-100002-22-21111-1-1-1i3i3−i3−i3i3i3−i3−i300-22-22000022-2-2i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3-1-111-1-111-11-110000-22−i3i3−i3i3−i3i3i3−i31-11-11-11-1000000000000
χ602-2-22-22-100002-22-21111-1-1-1i3i3−i3−i3i3i3−i3−i300-22-220000-2-222i3−i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-111-1-1-11-1100002-2−i3i3−i3i3i3−i3−i3i31-11-1-11-11000000000000
χ612-2-22-22-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i3002-2-2222-2-20000i3−i3i3−i3-1-111-1-111−i3−i3i3i3i3i3−i3−i31-11-1002-200−i3i3i3−i3-11-11-111-1−i3i3i3−i3000000000000
χ622-2-22-22-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i3002-2-22-2-2220000i3−i3i3−i311-1-111-1-1i3i3−i3−i3−i3−i3i3i31-11-100-2200−i3i3i3−i31-11-1-111-1i3−i3−i3i3000000000000
χ632-2-22-22-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i300-222-222-2-20000i3−i3i3−i3-1-111-1-111−i3−i3i3i3i3i3−i3−i31-11-100-2200i3−i3−i3i31-11-11-1-11i3−i3−i3i3000000000000
χ642-2-22-22-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i300-222-2-2-2220000i3−i3i3−i311-1-111-1-1i3i3−i3−i3−i3−i3i3i31-11-1002-200i3−i3−i3i3-11-111-1-11−i3i3i3−i3000000000000
χ652-2-22-22-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i3002-2-2222-2-20000−i3i3−i3i3-1-111-1-111i3i3−i3−i3−i3−i3i3i31-11-1002-200i3−i3−i3i3-11-11-111-1i3−i3−i3i3000000000000
χ662-2-22-22-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i3002-2-22-2-2220000−i3i3−i3i311-1-111-1-1−i3−i3i3i3i3i3−i3−i31-11-100-2200i3−i3−i3i31-11-1-111-1−i3i3i3−i3000000000000
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χ694444-4-4-244-4-444-4-4-2-22222-2-2-2-2-222224-4000000000000-2-2220000000000000000-2-2220000000000000000000000000000000000
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χ7644-4-400400−4i4i00004-40000-40000−4i4i−4i4i000000−2i2i−2i2i2-22-20000−2i2i−2i2i−2i2i−2i2i2-22-22-22-200000000000000000000000000000000000000
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χ7844-4-400-2004i−4i0000-22−2i32i3−2i32i3223−2323−23−2i2i−2i2i000000−2i2i−2i2i-22-220000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ111−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i300000000000000000000000000000000000000
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χ974-4-444-4400004-4-44-4-444-4-440000000000000000000000000000000000000000004-4-440000000000000000000000000000000000
χ984-4-444-440000-444-4-4-444-4-44000000000000000000000000000000000000000000-444-40000000000000000000000000000000000
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χ1014-4-444-4-20000-444-422-2-222-2−2i3−2i32i32i32i32i3−2i3−2i3000000000000002i3−2i3−2i32i300000000000000002-2-220000000000000000000000000000000000
χ1024-4-444-4-20000-444-422-2-222-22i32i3−2i3−2i3−2i3−2i32i32i300000000000000−2i32i32i3−2i300000000000000002-2-220000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.