Finite Group Databasebeta

← Group #10824876

Character table — Group #10824876

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122244442234444444444666121212126612121212121212121212244444446688881212121212121212121212121212242424242424242488888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1111-11-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1111-11-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1111-11-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ121111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1111-11-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ131111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-111-11-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ141111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-111-11-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ151111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-111-11-11-1-111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ161111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-111-11-11-1-111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-2-2-2-2-1-1-1-1-1-1111111111111111100000000000000000000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211-2-2-2-2111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211222211111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-22-2-222-2-222-2-22222222-2-2-2-2-2-222-2-22222-2-2000022000022-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-22-2-222-2-222-2-22222222-2-2-2-2-2-222-2-222-2-2220000-2-20000-2-22222000000000000000000000000000000000000
χ2522222222-2-22-2-2-2-222-2-2222222222-2-2-2-222-2-222-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2622222222-2-22-2-2-2-222-2-2222222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2722222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-122-2-20000-1-10000-1-11111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2822222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-122-2-20000-1-10000-1-11111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2922222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-1-2-222000011000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-1-2-222000011000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ312222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ322222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ332222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-11111-1-12-22-222-2-2-1-122-2-211-1-111-1-1-1-11111-1-1-1-1111100000000000000000000
χ342222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-11111-1-12-22-2-2-222-1-1-2-22211-1-1111111-1-1-1-11111-1-1-1-100000000000000000000
χ352222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-11111-1-1-22-2222-2-211-2-222-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ362222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-11111-1-1-22-22-2-2221122-2-2-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ372222-2-2-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000000022-2-2-2-222000000000000
χ382222-2-2-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000-2-22222-2-2000000000000
χ392222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-222-2-2-2-222222-2-220000220000-2-2-2-222000000000000000000000000000000000000
χ402222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-222-2-2-2-22222-222-20000-2-200002222-2-2000000000000000000000000000000000000
χ412222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-12-2-220000-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ422222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-12-2-220000-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ432222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-1-222-20000110000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ442222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-1-222-20000110000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-20000000000000000000000000000000000000000000000002i−2i2-20000
χ462-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-2000000000000000000000000000000000000000000000000−2i2i-220000
χ472-22-22i2i−2i−2i2-222i−2i−2i2i−2i2i-22-22-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-2200002-22i−2i0000000000002-22-22i−2i2i−2i0000000000000000000000000000
χ482-22-22i2i−2i−2i2-222i−2i−2i2i−2i2i-22-22-22-22i2i−2i−2i2-22i−2i-22−2i2i−2i2i-220000-22−2i2i000000000000-22-22−2i2i−2i2i0000000000000000000000000000
χ492-22-22i2i−2i−2i2-2-12i−2i−2i2i−2i2i-22-221-11−i−iii-11−ii1-1i−ii−i1-100002-22i−2i−i3i300003−3−i3i33−3-11-11−ii−ii−i3i3−i3i33−33−300000000000000000000
χ502-22-22i2i−2i−2i2-2-12i−2i−2i2i−2i2i-22-221-11−i−iii-11−ii1-1i−ii−i1-100002-22i−2ii3−i30000−33i3−i3−33-11-11−ii−iii3−i3i3−i3−33−3300000000000000000000
χ512-22-22i2i−2i−2i2-2-12i−2i−2i2i−2i2i-22-221-11−i−iii-11−ii1-1i−ii−i1-10000-22−2i2i−i3i300003−3−i3i33−31-11-1i−ii−ii3−i3i3−i3−33−3300000000000000000000
χ522-22-22i2i−2i−2i2-2-12i−2i−2i2i−2i2i-22-221-11−i−iii-11−ii1-1i−ii−i1-10000-22−2i2ii3−i30000−33i3−i3−331-11-1i−ii−i−i3i3−i3i33−33−300000000000000000000
χ532-22-22i2i−2i−2i-222−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i-222i−2i−2i2i2-2000000000000000000000000000000000000000000002i−2i2-200000000
χ542-22-22i2i−2i−2i-222−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i-222i−2i−2i2i2-200000000000000000000000000000000000000000000−2i2i-2200000000
χ552-22-22i2i−2i−2i-222−2i2i−2i2i2i−2i-222-2-22-22i2i−2i−2i-22−2i2i2-2−2i2i2i−2i-2200000000002-22i−2i000000000000002-2-222i−2i−2i2i00000000000000000000
χ562-22-22i2i−2i−2i-222−2i2i−2i2i2i−2i-222-2-22-22i2i−2i−2i-22−2i2i2-2−2i2i2i−2i-220000000000-22−2i2i00000000000000-222-2−2i2i2i−2i00000000000000000000
χ572-22-22i2i−2i−2i-22-1−2i2i−2i2i2i−2i-222-21-11−i−iii1-1i−i-11i−i−ii1-100000000−i3i32-22i−2i3−3i3−i3−33−i3i3i3−i33−3−33-111-1−iii−i00000000000000000000
χ582-22-22i2i−2i−2i-22-1−2i2i−2i2i2i−2i-222-21-11−i−iii1-1i−i-11i−i−ii1-100000000−i3i3-22−2i2i3−3i3−i3−33i3−i3−i3i3−333−31-1-11i−i−ii00000000000000000000
χ592-22-22i2i−2i−2i-22-1−2i2i−2i2i2i−2i-222-21-11−i−iii1-1i−i-11i−i−ii1-100000000i3−i32-22i−2i−33−i3i33−3i3−i3−i3i3−333−3-111-1−iii−i00000000000000000000
χ602-22-22i2i−2i−2i-22-1−2i2i−2i2i2i−2i-222-21-11−i−iii1-1i−i-11i−i−ii1-100000000i3−i3-22−2i2i−33−i3i33−3−i3i3i3−i33−3−331-1-11i−i−ii00000000000000000000
χ612-22-2−2i−2i2i2i2-22−2i2i2i−2i2i−2i-22-22-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-2200002-2−2i2i0000000000002-22-2−2i2i−2i2i0000000000000000000000000000
χ622-22-2−2i−2i2i2i2-22−2i2i2i−2i2i−2i-22-22-22-2−2i−2i2i2i2-2−2i2i-222i−2i2i−2i-220000-222i−2i000000000000-22-222i−2i2i−2i0000000000000000000000000000
χ632-22-2−2i−2i2i2i2-22−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-20000000000000000000000000000000000000000000000002i−2i-220000
χ642-22-2−2i−2i2i2i2-22−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-2000000000000000000000000000000000000000000000000−2i2i2-20000
χ652-22-2−2i−2i2i2i2-2-1−2i2i2i−2i2i−2i-22-221-11ii−i−i-11i−i1-1−ii−ii1-100002-2−2i2i−i3i30000−33−i3i3−33-11-11i−ii−i−i3i3−i3i3−33−3300000000000000000000
χ662-22-2−2i−2i2i2i2-2-1−2i2i2i−2i2i−2i-22-221-11ii−i−i-11i−i1-1−ii−ii1-100002-2−2i2ii3−i300003−3i3−i33−3-11-11i−ii−ii3−i3i3−i33−33−300000000000000000000
χ672-22-2−2i−2i2i2i2-2-1−2i2i2i−2i2i−2i-22-221-11ii−i−i-11i−i1-1−ii−ii1-10000-222i−2i−i3i30000−33−i3i3−331-11-1−ii−iii3−i3i3−i33−33−300000000000000000000
χ682-22-2−2i−2i2i2i2-2-1−2i2i2i−2i2i−2i-22-221-11ii−i−i-11i−i1-1−ii−ii1-10000-222i−2ii3−i300003−3i3−i33−31-11-1−ii−ii−i3i3−i3i3−33−3300000000000000000000
χ692-22-2−2i−2i2i2i-2222i−2i2i−2i−2i2i-222-2-22-2−2i−2i2i2i-222i−2i2-22i−2i−2i2i-2200000000002-2−2i2i000000000000002-2-22−2i2i2i−2i00000000000000000000
χ702-22-2−2i−2i2i2i-2222i−2i2i−2i−2i2i-222-2-22-2−2i−2i2i2i-222i−2i2-22i−2i−2i2i-220000000000-222i−2i00000000000000-222-22i−2i−2i2i00000000000000000000
χ712-22-2−2i−2i2i2i-2222i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i-22−2i2i2i−2i2-2000000000000000000000000000000000000000000002i−2i-2200000000
χ722-22-2−2i−2i2i2i-2222i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i-22−2i2i2i−2i2-200000000000000000000000000000000000000000000−2i2i2-200000000
χ732-22-2−2i−2i2i2i-22-12i−2i2i−2i−2i2i-222-21-11ii−i−i1-1−ii-11−iii−i1-100000000−i3i32-2−2i2i−33i3−i33−3−i3i3i3−i3−333−3-111-1i−i−ii00000000000000000000
χ742-22-2−2i−2i2i2i-22-12i−2i2i−2i−2i2i-222-21-11ii−i−i1-1−ii-11−iii−i1-100000000−i3i3-222i−2i−33i3−i33−3i3−i3−i3i33−3−331-1-11−iii−i00000000000000000000
χ752-22-2−2i−2i2i2i-22-12i−2i2i−2i−2i2i-222-21-11ii−i−i1-1−ii-11−iii−i1-100000000i3−i32-2−2i2i3−3−i3i3−33i3−i3−i3i33−3−33-111-1i−i−ii00000000000000000000
χ762-22-2−2i−2i2i2i-22-12i−2i2i−2i−2i2i-222-21-11ii−i−i1-1−ii-11−iii−i1-100000000i3−i3-222i−2i3−3−i3i3−33−i3i3i3−i3−333−31-1-11−iii−i00000000000000000000
χ774444444444-244-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-2-4-4-4-444-4-444-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-2-4-44444-4-4-4-4-2-2-22222-2-22222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-4-24444-4-4-4-444-2-2-2222222-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ8144-4-44-44-400400000000004-4-44-44-40000000000000000000000000000000000000000000000000022−220022−22000000000000
χ8244-4-44-44-400400000000004-4-44-44-400000000000000000000000000000000000000000000000000−222200−2222000000000000
χ8344-4-4-44-4400400000000004-4-4-44-440000000000000000000000000000000000000000000000000022−2200−2222000000000000
χ8444-4-4-44-4400400000000004-4-4-44-4400000000000000000000000000000000000000000000000000−22220022−22000000000000
χ854-44-44i4i−4i−4i4-4-24i−4i4i−4i4i−4i4-44-42-22−2i−2i2i2i-22−2i2i-22−2i2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ864-44-44i4i−4i−4i-44-2−4i4i4i−4i−4i4i4-4-442-22−2i−2i2i2i2-22i−2i2-2−2i2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ874-44-4−4i−4i4i4i4-4-2−4i4i−4i4i−4i4i4-44-42-222i2i−2i−2i-222i−2i-222i−2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ884-44-4−4i−4i4i4i-44-24i−4i−4i4i4i−4i4-4-442-222i2i−2i−2i2-2−2i2i2-22i−2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ894-4-444i−4i−4i4i0040000000000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000−2i22i20022−2200000000000000
χ904-4-444i−4i−4i4i0040000000000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002i2−2i200−222200000000000000
χ914-4-44−4i4i4i−4i0040000000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000−2i22i200−222200000000000000
χ924-4-44−4i4i4i−4i0040000000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002i2−2i20022−2200000000000000
χ9388-8-88-88-800-40000000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-88-8800-40000000000-4444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-4000000000044-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-4000000000044-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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