Finite Group Databasebeta

← Group #10702900

Character table — Group #10702900

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122244442222223444444666121212126666661212121212122244666688888888121212122424242424242424242424242424242444444444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ91111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii
χ111111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−i
χ131111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ151111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-2-222-2-2-22-2222222222-2-2-2-22-2-2-22-20000000000000000000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-222-2-2-22-2222222222-2-2-2-22-2-2-22-2000000000000000000000000000000000000000000000000-22-220000
χ2322222222-2-222-2-22-22-2-2-222222222-2-222-2-2-22-2-2-2200000000000000000000000000000000000000000000000000002-22-2
χ2422222222-2-222-2-22-22-2-2-222222222-2-222-2-2-22-2-2-220000000000000000000000000000000000000000000000000000-22-22
χ2522222222-2-2-2-2222-2-222-2-22222222-2-2-2-222-2-222-2-22-2-2222-2-200000000-2-222000000000000000000000000000000000000
χ2622222222-2-2-2-2222-2-222-2-22222222-2-2-2-222-2-222-2-2-222-2-2-2220000000022-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1112-2-22-1-1110000000011-1-133−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1112-2-22-1-1110000000011-1-1−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-111-222-211-1-100000000-1-11133−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-111-222-211-1-100000000-1-111−3−333−3−33333−3−333−3−300000000000000000000
χ312222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-1112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ322222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-111−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ342222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ352222-2-2-2-222-2-2-2-22-2222-22222-2-2-2-222-2-2-2-2-2222-220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-222-2-2-2-22-2222-22222-2-2-2-222-2-2-2-2-2222-22000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-2-222-2-222-2222-2222-2-2-2-2-2-222-2-22-2222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ382222-2-2-2-2-2-222-2-222-2222-2222-2-2-2-2-2-222-2-22-2222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ392222-2-2-2-2-2-2-2-222222-2-222222-2-2-2-2-2-2-2-22222-2-22222-2-2222200000000-2-2-2-2000000000000000000000000000000000000
χ402222-2-2-2-2-2-2-2-222222-2-222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-2000000002222000000000000000000000000000000000000
χ412222-2-2-2-2-2-2-2-222-122-2-222-1-1-111111111-1-1-1-111-1-122-2-2-1-1-1-1000000001111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ422222-2-2-2-2-2-2-2-222-122-2-222-1-1-111111111-1-1-1-111-1-122-2-2-1-1-1-1000000001111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ432222-2-2-2-2-2-2-2-222-122-2-222-1-1-111111111-1-1-1-111-1-1-2-222111100000000-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ442222-2-2-2-2-2-2-2-222-122-2-222-1-1-111111111-1-1-1-111-1-1-2-222111100000000-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4522-2-222-2-22-22-22-222-22-2-22-2-2222-2-22-22-22-22-22-2-22000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ4622-2-222-2-22-22-22-222-22-2-22-2-2222-2-22-22-22-22-22-2-2200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ4722-2-222-2-22-2-22-22222-22-2-2-2-2222-2-22-2-22-2222-22-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4822-2-222-2-22-2-22-22222-22-2-2-2-2222-2-22-2-22-2222-22-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4922-2-222-2-22-2-22-22-122-22-2-211-1-1-111-111-11-1-1-11-1110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii00000000000000000000
χ5022-2-222-2-22-2-22-22-122-22-2-211-1-1-111-111-11-1-1-11-1110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i00000000000000000000
χ5122-2-222-2-22-2-22-22-122-22-2-211-1-1-111-111-11-1-1-11-1110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−33−33−33−33−ii−ii−ii−ii00000000000000000000
χ5222-2-222-2-22-2-22-22-122-22-2-211-1-1-111-111-11-1-1-11-1110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i33−33−33−33−3i−ii−ii−ii−i00000000000000000000
χ5322-2-222-2-2-222-2-222-2-2-2222-2-2222-2-2-222-2-22-2-2-2222000000002-22-2000000002-2-222-2-220000000000000000000000000000
χ5422-2-222-2-2-222-2-222-2-2-2222-2-2222-2-2-222-2-22-2-2-222200000000-22-2200000000-222-2-222-20000000000000000000000000000
χ5522-2-222-2-2-222-2-22-1-2-2-222211-1-1-1111-1-111-1111-1-1-10000−i3i3i3−i32-22-20000i3−i3−i3i3-111-1-111-1−i3i3i3−i3−i3i3i3−i300000000000000000000
χ5622-2-222-2-2-222-2-22-1-2-2-222211-1-1-1111-1-111-1111-1-1-10000−i3i3i3−i3-22-220000i3−i3−i3i31-1-111-1-11i3−i3−i3i3i3−i3−i3i300000000000000000000
χ5722-2-222-2-2-222-2-22-1-2-2-222211-1-1-1111-1-111-1111-1-1-10000i3−i3−i3i32-22-20000−i3i3i3−i3-111-1-111-1i3−i3−i3i3i3−i3−i3i300000000000000000000
χ5822-2-222-2-2-222-2-22-1-2-2-222211-1-1-1111-1-111-1111-1-1-10000i3−i3−i3i3-22-220000−i3i3i3−i31-1-111-1-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ5922-2-222-2-2-22-222-22-222-22-2-2-2222-2-2-22-222-2-222-22-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ6022-2-222-2-2-22-222-22-222-22-2-2-2222-2-2-22-222-2-222-22-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ6122-2-2-2-2222-22-22-22-22-222-2-2-22-2-2222-22-22-2-22-222-2000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ6222-2-2-2-2222-22-22-22-22-222-2-2-22-2-2222-22-22-2-22-222-200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ6322-2-2-2-2222-2-22-222-2-22-222-2-22-2-2222-2-22-22-2-22-2220000000000002-2-220000000000002-22-2-22-2200000000000000000000
χ6422-2-2-2-2222-2-22-222-2-22-222-2-22-2-2222-2-22-22-2-22-222000000000000-222-2000000000000-22-222-22-200000000000000000000
χ6522-2-2-2-2222-2-22-22-1-2-22-22211-111-1-1-111-11-111-11-1-10000−i3i3i3−i300002-2-22−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3-11-111-11-100000000000000000000
χ6622-2-2-2-2222-2-22-22-1-2-22-22211-111-1-1-111-11-111-11-1-10000−i3i3i3−i30000-222-2−i3i3i3−i3i3−i3i3−i3−i3i3−i3i31-11-1-11-1100000000000000000000
χ6722-2-2-2-2222-2-22-22-1-2-22-22211-111-1-1-111-11-111-11-1-10000i3−i3−i3i300002-2-22i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3-11-111-11-100000000000000000000
χ6822-2-2-2-2222-2-22-22-1-2-22-22211-111-1-1-111-11-111-11-1-10000i3−i3−i3i30000-222-2i3−i3−i3i3−i3i3−i3i3i3−i3i3−i31-11-1-11-1100000000000000000000
χ6922-2-2-2-222-222-2-222222-2-2-2-2-22-2-222-222-2-22222-2-2-2000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ7022-2-2-2-222-222-2-222222-2-2-2-2-22-2-222-222-2-22222-2-2-200000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ7122-2-2-2-222-222-2-22-1222-2-2-211-111-1-11-1-111-1-1-1-11110000−i3i3−i3i32i−2i−2i2i0000i3−i3i3−i3−iii−ii−i−ii3−3−33−333−300000000000000000000
χ7222-2-2-2-222-222-2-22-1222-2-2-211-111-1-11-1-111-1-1-1-11110000−i3i3−i3i3−2i2i2i−2i0000i3−i3i3−i3i−i−ii−iii−i−333−33−3−3300000000000000000000
χ7322-2-2-2-222-222-2-22-1222-2-2-211-111-1-11-1-111-1-1-1-11110000i3−i3i3−i32i−2i−2i2i0000−i3i3−i3i3−iii−ii−i−ii−333−33−3−3300000000000000000000
χ7422-2-2-2-222-222-2-22-1222-2-2-211-111-1-11-1-111-1-1-1-11110000i3−i3i3−i3−2i2i2i−2i0000−i3i3−i3i3i−i−ii−iii−i3−3−33−333−300000000000000000000
χ7522-2-2-2-222-22-222-222-2-22-22-2-22-2-222-22-222-22-2-22-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ7622-2-2-2-222-22-222-222-2-22-22-2-22-2-222-22-222-22-2-22-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ774444444444-4-4-4-4-24-4-4-44-4-2-2-2-2-2-2-2-2-22222-2222-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-444-4-4-2-44-4-4-44-2-2-2-2-2-2-222-2-2222-2222-200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-4-4-4-4-2-4444-44-2-2-22222-2-222222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-444-4-4-24-4444-4-2-2-2222222-2-222-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ8144-4-444-4-44-44-44-4-24-44-4-4422-2-2-222-22-22-22-22-222-200000000000000000000000000000000000000000000000000000000
χ8244-4-444-4-4-44-444-4-2-444-44-422-2-2-2222-22-2-222-2-22-2200000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-4444-44-44-4-2-44-444-422-222-2-2-22-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-444-4-24-4-44-4422-222-2-22-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ854-44-44i−4i4i−4i00000040000004-4-44i−4i4i−4i0000000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ864-44-44i−4i4i−4i00000040000004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ874-44-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ884-44-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ894-4-444i−4i−4i4i0000004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002i−2i−2i2i-222-2000000000000
χ904-4-444i−4i−4i4i0000004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ914-4-44−4i4i4i−4i0000004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ924-4-44−4i4i4i−4i0000004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2000000000000
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 i is the imaginary unit (i² = −1).