Finite Group Databasebeta

← Group #10702235

Character table — Group #10702235

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122244442222223444444666121212126666661212121212122244444466668888121212121212121212121212242424242424242488888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−i1111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−i1111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii1111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i-1-111
χ121111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii1111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-1-111
χ141111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i11-1-1
χ151111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iii-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii11-1-1
χ161111-1-1-1-111-1-1-1-11111-11-1111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iii-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-2-22-2-2-22-22222222222-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-22-2-2-22-22222222222-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000000000-22-220000
χ2322222222-2-222-2-222-2-2-22-22222222-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000002-22-200000000
χ2422222222-2-222-2-222-2-2-22-22222222-2-222-2-222-2-2-2-200000000000000000000000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2222-222-2-2-22222222-2-2-2-222-2-222-2-20000000000002-22-200000000000022-2-222-2-200000000000000000000
χ2622222222-2-2-2-2222-222-2-2-22222222-2-2-2-222-2-222-2-2000000000000-22-22000000000000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000−i3−i3i3i32-22-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000000000
χ2822222222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000−i3−i3i3i3-22-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000000000
χ2922222222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000i3i3−i3−i32-22-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000000000
χ3022222222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000i3i3−i3−i3-22-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000000000
χ312222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ332222-2-2-2-222-2-2-2-2-1222-22-2-1-1-11111-1-11111-1-1-1-11122-2-22i2i−2i−2i-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ342222-2-2-2-222-2-2-2-2-1222-22-2-1-1-11111-1-11111-1-1-1-11122-2-2−2i−2i2i2i-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ352222-2-2-2-222-2-2-2-2-1222-22-2-1-1-11111-1-11111-1-1-1-111-2-2222i2i−2i−2i1111−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ362222-2-2-2-222-2-2-2-2-1222-22-2-1-1-11111-1-11111-1-1-1-111-2-222−2i−2i2i2i11112i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ372222-2-2-2-2-2-222-2-22-2222-22222-2-2-2-2-2-222-2-2-2-222220000000000002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ382222-2-2-2-2-2-222-2-22-2222-22222-2-2-2-2-2-222-2-2-2-22222000000000000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ392222-2-2-2-2-2-222-2-2-1-2222-22-1-1-1111111-1-11111-1-1-1-100000000−i3−i3i3i32i−2i−2i2ii3i3−i3−i333−3−3−3−333−i−iiiii−i−i00000000000000000000
χ402222-2-2-2-2-2-222-2-2-1-2222-22-1-1-1111111-1-11111-1-1-1-100000000−i3−i3i3i3−2i2i2i−2ii3i3−i3−i3−3−33333−3−3ii−i−i−i−iii00000000000000000000
χ412222-2-2-2-2-2-222-2-2-1-2222-22-1-1-1111111-1-11111-1-1-1-100000000i3i3−i3−i32i−2i−2i2i−i3−i3i3i3−3−33333−3−3−i−iiiii−i−i00000000000000000000
χ422222-2-2-2-2-2-222-2-2-1-2222-22-1-1-1111111-1-11111-1-1-1-100000000i3i3−i3−i3−2i2i2i−2i−i3−i3i3i333−3−3−3−333ii−i−i−i−iii00000000000000000000
χ432222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22222-2-222000000000000000000000000000000000000000000002-2-2200000000
χ442222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000000000000000-222-200000000
χ4522-2-222-2-22-22-22-2222-22-2-2-2-2222-2-22-22-22-22-22-22-22-22-200002-22-200002-22-2000000000000000000000000000000000000
χ4622-2-222-2-22-22-22-2222-22-2-2-2-2222-2-22-22-22-22-22-22-2-22-220000-22-220000-22-22000000000000000000000000000000000000
χ4722-2-222-2-22-22-22-2-122-22-2-211-1-1-111-11-11-11-11-11-112-22-20000-11-110000-11-113−33−33−33−33−33−33−33−300000000000000000000
χ4822-2-222-2-22-22-22-2-122-22-2-211-1-1-111-11-11-11-11-11-112-22-20000-11-110000-11-11−33−33−33−33−33−33−33−3300000000000000000000
χ4922-2-222-2-22-22-22-2-122-22-2-211-1-1-111-11-11-11-11-11-11-22-2200001-11-100001-11-13−33−33−33−3−33−33−33−3300000000000000000000
χ5022-2-222-2-22-22-22-2-122-22-2-211-1-1-111-11-11-11-11-11-11-22-2200001-11-100001-11-1−33−33−33−333−33−33−33−300000000000000000000
χ5122-2-222-2-22-2-22-222-2-2222-2-2-2222-2-22-2-22-22-22-222-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ5222-2-222-2-22-2-22-222-2-2222-2-2-2222-2-22-2-22-22-22-222-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ5322-2-222-2-2-222-2-2222-22-2-22-2-2222-2-2-222-2-222-2-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ5422-2-222-2-2-222-2-2222-22-2-22-2-2222-2-2-222-2-222-2-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ5522-2-222-2-2-22-222-22-22-2-222-2-2222-2-2-22-222-2-222-2-2200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ5622-2-222-2-2-22-222-22-22-2-222-2-2222-2-2-22-222-2-222-2-220000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ5722-2-222-2-2-22-222-2-1-22-2-22211-1-1-1111-11-1-111-1-111-100002i−2i2i−2i−i3i3i3−i30000−i3i3i3−i3−iii−i−iii−i3−3−333−3−3300000000000000000000
χ5822-2-222-2-2-22-222-2-1-22-2-22211-1-1-1111-11-1-111-1-111-100002i−2i2i−2ii3−i3−i3i30000i3−i3−i3i3−iii−i−iii−i−333−3−333−300000000000000000000
χ5922-2-222-2-2-22-222-2-1-22-2-22211-1-1-1111-11-1-111-1-111-10000−2i2i−2i2i−i3i3i3−i30000−i3i3i3−i3i−i−iii−i−ii−333−3−333−300000000000000000000
χ6022-2-222-2-2-22-222-2-1-22-2-22211-1-1-1111-11-1-111-1-111-10000−2i2i−2i2ii3−i3−i3i30000i3−i3−i3i3i−i−iii−i−ii3−3−333−3−3300000000000000000000
χ6122-2-2-2-2222-22-22-22-2-22-222-2-22-2-2222-22-22-2-22-22-2200000000000000000000000000000000000022-2-2-2-222000000000000
χ6222-2-2-2-2222-22-22-22-2-22-222-2-22-2-2222-22-22-2-22-22-22000000000000000000000000000000000000-2-22222-2-2000000000000
χ6322-2-2-2-2222-2-22-22222-2-2-22-2-22-2-2222-2-22-222-22-2-222-2-2200002-22-20000-22-22000000000000000000000000000000000000
χ6422-2-2-2-2222-2-22-22222-2-2-22-2-22-2-2222-2-22-222-22-2-22-222-20000-22-2200002-22-2000000000000000000000000000000000000
χ6522-2-2-2-2222-2-22-22-122-2-2-2211-111-1-1-111-11-1-11-111-12-2-220000-11-1100001-11-1−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i300000000000000000000
χ6622-2-2-2-2222-2-22-22-122-2-2-2211-111-1-1-111-11-1-11-111-12-2-220000-11-1100001-11-1i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i300000000000000000000
χ6722-2-2-2-2222-2-22-22-122-2-2-2211-111-1-1-111-11-1-11-111-1-222-200001-11-10000-11-11−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i300000000000000000000
χ6822-2-2-2-2222-2-22-22-122-2-2-2211-111-1-1-111-11-1-11-111-1-222-200001-11-10000-11-11i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i300000000000000000000
χ6922-2-2-2-222-222-2-222-22-222-2-2-22-2-222-222-2-22-222-22-200002-2-220000000000002-2-22-222-20000000000000000000000000000
χ7022-2-2-2-222-222-2-222-22-222-2-2-22-2-222-222-2-22-222-22-20000-222-2000000000000-222-22-2-220000000000000000000000000000
χ7122-2-2-2-222-222-2-22-1-22-222-211-111-1-11-1-111-11-1-11-1100002-2-22−i3i3i3−i30000i3−i3−i3i3-111-11-1-11−i3i3i3−i3i3−i3−i3i300000000000000000000
χ7222-2-2-2-222-222-2-22-1-22-222-211-111-1-11-1-111-11-1-11-1100002-2-22i3−i3−i3i30000−i3i3i3−i3-111-11-1-11i3−i3−i3i3−i3i3i3−i300000000000000000000
χ7322-2-2-2-222-222-2-22-1-22-222-211-111-1-11-1-111-11-1-11-110000-222-2−i3i3i3−i30000i3−i3−i3i31-1-11-111-1i3−i3−i3i3−i3i3i3−i300000000000000000000
χ7422-2-2-2-222-222-2-22-1-22-222-211-111-1-11-1-111-11-1-11-110000-222-2i3−i3−i3i30000−i3i3i3−i31-1-11-111-1−i3i3i3−i3i3−i3−i3i300000000000000000000
χ7522-2-2-2-222-22-222-222-222-2-2-2-22-2-222-22-222-22-2-222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ7622-2-2-2-222-22-222-222-222-2-2-2-22-2-222-22-222-22-2-222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774444444444-4-4-4-4-2-4-4-44-44-2-2-2-2-2-2-2-2-222222222-2-200000000000000000000000000000000000000000000000000000000
χ7844444444-4-444-4-4-24-4-4-44-4-2-2-2-2-2-2-222-2-222-2-2222200000000000000000000000000000000000000000000000000000000
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χ804444-4-4-4-4-4-4-4-444-24-4-4444-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000000000000000000000000000
χ8144-4-444-4-44-4-44-44-2-4-4444-422-2-2-222-222-22-22-22-2-2200000000000000000000000000000000000000000000000000000000
χ8244-4-444-4-4-444-4-44-24-44-4-4422-2-2-2222-2-222-2-222-22-200000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-4444-44-44-4-2-4-44-44422-222-2-2-22-22-222-22-22-200000000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-444-4-24-444-4-422-222-2-22-22-2-22-222-2-2200000000000000000000000000000000000000000000000000000000
χ854-44-44i−4i4i−4i00000040000004-4-44i−4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ864-44-44i−4i4i−4i00000040000004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ874-44-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ884-44-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ894-4-444i−4i−4i4i0000004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ904-4-444i−4i−4i4i0000004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ914-4-44−4i4i4i−4i0000004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ924-4-44−4i4i4i−4i0000004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ938-88-88i−8i8i−8i000000-4000000-444−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8−8i8i−8i8i000000-4000000-4444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i000000-40000004-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i000000-40000004-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.