Finite Group Databasebeta

← Group #11923247

Character table — Group #11923247

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order1222223666334466666666121212122222443366666666662244412126666121212121212121212121212446666666661212444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1111111111111111-11-11111111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1
χ3111111111111-1-111111111-1-1-1-1111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111111111-11-11-1-1-1-1-1
χ4111111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111
χ51111111111−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1+i32−1−i32−1+i32
χ61111111111−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-11+i321−i321+i321−i32
χ71111111111−1−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11-11-11+i321−i321+i321−i32
χ81111111111−1−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-11111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-111-11−1−i32−1+i32−1−i32−1+i32
χ91111111111−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1−i32−1+i32−1−i32
χ101111111111−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-11−i321+i321−i321+i32
χ111111111111−1+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11-11-11−i321+i321−i321+i32
χ121111111111−1+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-11111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-111-11−1+i32−1−i32−1+i32−1−i32
χ131111-1-11111111-1-1-111111111-1-111-1-11111-1-1-1-1111111-111-1-111-1-1-1-11-11-111-1-111-1-1-1-1-111-1-111-1-11-1-11111-1-1
χ141111-1-11111111-1-1-111111111-1-1-1-1111111-1-1-1-1111111-1-111-111-1-1-1-11-11-111-1-111-1-111-1-1-111-1-1111-11-1-1-1-111
χ151111-1-1111111-11-1-1111111-1-11111-1-11111-1-1-1-11111111-1-11-111-1-1-1-1-11-11-1-111-1-111-1-1111-1-111-1-1-1-111-1-1-111
χ161111-1-1111111-11-1-1111111-1-111-1-1111111-1-1-1-111111111-1-1-111-1-1-1-1-11-11-1-111-1-111111-1-111-1-111-1-1-1-1111-1-1
χ171111-1-11111−1−i32−1+i321-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-1-1111+i321+i321−i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-111−1−i32−1+i321+i321−i32
χ181111-1-11111−1−i32−1+i321-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-1-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1111+i321+i321−i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11-1-11+i321−i32−1−i32−1+i32
χ191111-1-11111−1−i32−1+i32-11-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1111+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-111-11+i321−i32−1−i32−1+i32
χ201111-1-11111−1−i32−1+i32-11-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1111+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-1-11−1−i32−1+i321+i321−i32
χ211111-1-11111−1+i32−1−i321-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-1-1111−i321−i321+i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-111−1+i32−1−i321−i321+i32
χ221111-1-11111−1+i32−1−i321-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-1-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1111−i321−i321+i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11-1-11−i321+i32−1+i32−1−i32
χ231111-1-11111−1+i32−1−i32-11-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-11111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1111−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-111-11−i321+i32−1+i32−1−i32
χ241111-1-11111−1+i32−1−i32-11-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1111−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-1-11−1+i32−1−i321−i321+i32
χ25222222-1-1-1-12222-1-1222222-1-1-1-1000022-1-12222-1-1-1-1-1-120202-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-100000000-1-10000000
χ26222222-1-1-1-122-2-2-1-12222221111000022-1-12222-1-1-1-1-1-1-20-202-1-1-1-1-1-1-2-2-2-211111111001000000001-10000000
χ27222222-1-1-1-1−1−i3−1+i322-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-1-1-10000221+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i3220202-1-11+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i3200-100000000-1-10000000
χ28222222-1-1-1-1−1−i3−1+i3-2-2-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i311110000221+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i32-20-202-1-11+i321+i321−i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32001000000001-10000000
χ29222222-1-1-1-1−1+i3−1−i322-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-1-1-10000221−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i3220202-1-11−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i3200-100000000-1-10000000
χ30222222-1-1-1-1−1+i3−1−i3-2-2-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i311110000221−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i32-20-202-1-11−i321−i321+i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32001000000001-10000000
χ312222-2-2-1-1-1-1222-211222222-1-111000022-1-1-2-2-2-2-1-1-1-1-1-1-2020-2-1-111112-22-2-1-111-1-11100100000000-110000000
χ322222-2-2-1-1-1-122-221122222211-1-1000022-1-1-2-2-2-2-1-1-1-1-1-120-20-2-1-11111-22-2211-1-111-1-100-100000000110000000
χ332222-2-2-1-1-1-1−1−i3−1+i32-211−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-1110000221+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i32-2020-2-1-1−1−i32−1−i32−1+i32−1+i32−1−i31+i3−1+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200100000000-110000000
χ342222-2-2-1-1-1-1−1−i3−1+i3-2211−1−i3−1−i3−1+i3−1+i3−1−i3−1+i311-1-10000221+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i3220-20-2-1-1−1−i32−1−i32−1+i32−1+i321+i3−1−i31−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200-100000000110000000
χ352222-2-2-1-1-1-1−1+i3−1−i32-211−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-1110000221−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i32-2020-2-1-1−1+i32−1+i32−1−i32−1−i32−1+i31−i3−1−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200100000000-110000000
χ362222-2-2-1-1-1-1−1+i3−1−i3-2211−1+i3−1+i3−1−i3−1−i3−1+i3−1−i311-1-10000221−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i3220-20-2-1-1−1+i32−1+i32−1−i32−1−i321−i3−1+i31+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200-100000000110000000
χ372-2-22002-2-222200002-22-2-2-20000002-22-2220000-2-22-22-2000002-200000000000000002-20002-2002-2000000000
χ382-2-22002-2-222200002-22-2-2-2000000-222-2220000-2-22-22-2000002-20000000000000000-22000-2200-22000000000
χ392-2-22002-2-22−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i30000002-22-2−1−i3−1+i300001+i31−i3−1−i31+i3−1+i31−i3000002-200000000000000002-2000−1−i31+i300−1+i31−i3000000000
χ402-2-22002-2-22−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i3000000-222-2−1−i3−1+i300001+i31−i3−1−i31+i3−1+i31−i3000002-20000000000000000-220001+i3−1−i3001−i3−1+i3000000000
χ412-2-22002-2-22−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i30000002-22-2−1+i3−1−i300001−i31+i3−1+i31−i3−1−i31+i3000002-200000000000000002-2000−1+i31−i300−1−i31+i3000000000
χ422-2-22002-2-22−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i3000000-222-2−1+i3−1−i300001−i31+i3−1+i31−i3−1−i31+i3000002-20000000000000000-220001−i3−1+i3001+i3−1−i3000000000
χ43333333333300333300000033333333-1-1000000000000-13-13-1-1-10000000000000000-1-1-100000000-1-1-1-1-10000
χ4433333333330033330000003333-3-3-3-3-1-1000000000000-1-3-1-3-1-1-1000000000000000011-100000000-1-11110000
χ45333333333300-3-333000000-3-3-3-33333-1-10000000000001-31-3-1-1-10000000000000000-1-11000000001-11-110000
χ46333333333300-3-333000000-3-3-3-3-3-3-3-3-1-10000000000001313-1-1-10000000000000000111000000001-1-11-10000
χ473333-3-33333003-3-3-300000033-3-333-3-3-1-100000000000013-1-31-1-1000000000000000011100000000-111-1-10000
χ483333-3-33333003-3-3-300000033-3-3-3-333-1-10000000000001-3-131-1-10000000000000000-1-1100000000-11-1110000
χ493333-3-3333300-33-3-3000000-3-33333-3-3-1-1000000000000-1-3131-1-1000000000000000011-10000000011-1-110000
χ503333-3-3333300-33-3-3000000-3-333-3-333-1-1000000000000-131-31-1-10000000000000000-1-1-1000000001111-10000
χ5144-4-44-44-44-4-2-2004-42222-2-20000000000-2-22-22-2-2-2222200000002-22-200000000000000000000000000000000
χ5244-4-44-44-44-41+i31−i3004-4−1−i3−1−i3−1+i3−1+i31+i31−i300000000001+i31−i3−1−i31+i3−1+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i30000000−1−i31+i3−1+i31−i300000000000000000000000000000000
χ5344-4-44-44-44-41−i31+i3004-4−1+i3−1+i3−1−i3−1−i31−i31+i300000000001−i31+i3−1+i31−i3−1−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i30000000−1+i31−i3−1−i31+i300000000000000000000000000000000
χ5444-4-44-4-22-22-2-200-222222-2-223−2323−23000000112-22-211-1-1-1-10000000-11-1100003−33−33−33−300000000000000000000
χ5544-4-44-4-22-22-2-200-222222-2-2−2323−2323000000112-22-211-1-1-1-10000000-11-110000−33−33−33−3300000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.