Finite Group Databasebeta

← Group #10823711

Character table — Group #10823711

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466666666666121212121212121224444444444466121212121212121212121212121212121212121212122244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-11-11-11-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-11-11-11-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-111-1-11-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-111-1-111-111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-22-2-2-2-2-2-2-1-1-1-111111111-1-11111-1-111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-222-2-2-2-211111111111111-1-1-1-111-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-1-1-1-1-1-1-11111111111110000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-2222-2-2-222-2-2-1-111-1-1-1-11111-1-1-1-1-1-11111110000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-2-2-222-2-222-1-1111111-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-2222-2-2-2-22211-1-11111-1-1-1-111-1-1-1-1-1-111110000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-2-2-222222-2-211-1-1-1-1-1-11111111111-1-1-1-1-1-10000000000000000
χ25222222-2-2-2-222222-2-2-2-22222222-2-2-2-22222-2-2-2-222-200-2000000222200000000-2-20000-2-200000000000000000000
χ26222222-2-2-2-222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-22002000000-2-2-2-2000000002200002200000000000000000000
χ27222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222222-2-200200000022-2-200000000-2-200002200000000000000000000
χ28222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-22222-22200-2000000-2-22200000000220000-2-200000000000000000000
χ29222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111122-200-2000000-1-1-1-1−i3−i3i3i3−i3−i3i3i311−i3−i3i3i311−i3−i3i3i30000000000000000
χ30222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111122-200-2000000-1-1-1-1i3i3−i3−i3i3i3−i3−i311i3i3−i3−i311i3i3−i3−i30000000000000000
χ31222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-2-220020000001111−i3−i3i3i3−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i30000000000000000
χ32222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-2-220020000001111i3i3−i3−i3i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i30000000000000000
χ33222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-12-2-2002000000-1-111−i3−i3i3i3i3i3−i3−i311−i3−i3i3i3-1-1i3i3−i3−i30000000000000000
χ34222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-12-2-2002000000-1-111i3i3−i3−i3−i3−i3i3i311i3i3−i3−i3-1-1−i3−i3i3i30000000000000000
χ35222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-22200-200000011-1-1−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i311−i3−i3i3i30000000000000000
χ36222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-22200-200000011-1-1i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i311i3i3−i3−i30000000000000000
χ372222-2-222-2-2222-2-222-2-22-2-2-2-22222-2-222-2-222-2-200000000000000000000000000000000000002020-20-200000000
χ382222-2-222-2-2222-2-222-2-22-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000000-20-2020200000000
χ392222-2-222-2-22-2-222-2-2222-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000020-20-20200000000
χ402222-2-222-2-22-2-222-2-2222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000000-202020-200000000
χ412222-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000000000000020-20-202000000000
χ422222-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-222000000000000000000000000000000000000-202020-2000000000
χ432222-2-2-2-2222-2-22222-2-22-2-2-2-222-2-222-2-22222-2-20000000000000000000000000000000000002020-20-2000000000
χ442222-2-2-2-2222-2-22222-2-22-2-2-2-222-2-222-2-22222-2-2000000000000000000000000000000000000-20-20202000000000
χ452-22-22-22-22-222i−2i2i−2i2i−2i2i−2i-222-2-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002i−2i2-2
χ462-22-22-22-22-222i−2i2i−2i2i−2i2i−2i-222-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2i2i-22
χ472-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002i−2i-22
χ482-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2i2i2-2
χ492-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000002-22i−2i0000
χ502-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000-22−2i2i0000
χ512-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000002-2−2i2i0000
χ522-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000-222i−2i0000
χ532-22-2-222-2-2222i−2i−2i2i2i−2i−2i2i-2-2-2222-22-2-222i−2i−2i2i2i−2i−2i2i0002-202i−2i0000000000000000002-22-2002i−2i2i−2i0000000000000000
χ542-22-2-222-2-2222i−2i−2i2i2i−2i−2i2i-2-2-2222-22-2-222i−2i−2i2i2i−2i−2i2i000-220−2i2i000000000000000000-22-2200−2i2i−2i2i0000000000000000
χ552-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i-2-2-2222-22-2-22−2i2i2i−2i−2i2i2i−2i0002-20−2i2i0000000000000000002-22-200−2i2i−2i2i0000000000000000
χ562-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i-2-2-2222-22-2-22−2i2i2i−2i−2i2i2i−2i000-2202i−2i000000000000000000-22-22002i−2i2i−2i0000000000000000
χ572-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i111-1-1-11-111-1−iii−i−iii−i0002-202i−2i0000−i3i33−3−i3i3−i3i33−33−3−i3i3-11-113−3−ii−ii0000000000000000
χ582-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i111-1-1-11-111-1−iii−i−iii−i0002-202i−2i0000i3−i3−33i3−i3i3−i3−33−33i3−i3-11-11−33−ii−ii0000000000000000
χ592-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i111-1-1-11-111-1−iii−i−iii−i000-220−2i2i0000−i3i33−3i3−i3i3−i3−33−33−i3i31-11-13−3i−ii−i0000000000000000
χ602-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i111-1-1-11-111-1−iii−i−iii−i000-220−2i2i0000i3−i3−33−i3i3−i3i33−33−3i3−i31-11-1−33i−ii−i0000000000000000
χ612-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i111-1-1-11-111-1i−i−iii−i−ii0002-20−2i2i0000−i3i3−33−i3i3−i3i3−33−33−i3i3-11-11−33i−ii−i0000000000000000
χ622-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i111-1-1-11-111-1i−i−iii−i−ii0002-20−2i2i0000i3−i33−3i3−i3i3−i33−33−3i3−i3-11-113−3i−ii−i0000000000000000
χ632-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i111-1-1-11-111-1i−i−iii−i−ii000-2202i−2i0000−i3i3−33i3−i3i3−i33−33−3−i3i31-11-1−33−ii−ii0000000000000000
χ642-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i111-1-1-11-111-1i−i−iii−i−ii000-2202i−2i0000i3−i33−3−i3i3−i3i3−33−33i3−i31-11-13−3−ii−ii0000000000000000
χ652-22-2-22-222-222i−2i−2i2i−2i2i2i−2i-2-2-2222-2-222-22i−2i−2i2i−2i2i2i−2i000000002-22i−2i00002-2-222i−2i−2i2i0000000000000000000000000000
χ662-22-2-22-222-222i−2i−2i2i−2i2i2i−2i-2-2-2222-2-222-22i−2i−2i2i−2i2i2i−2i00000000-22−2i2i0000-222-2−2i2i2i−2i0000000000000000000000000000
χ672-22-2-22-222-22−2i2i2i−2i2i−2i−2i2i-2-2-2222-2-222-2−2i2i2i−2i2i−2i−2i2i000000002-2−2i2i00002-2-22−2i2i2i−2i0000000000000000000000000000
χ682-22-2-22-222-22−2i2i2i−2i2i−2i−2i2i-2-2-2222-2-222-2−2i2i2i−2i2i−2i−2i2i00000000-222i−2i0000-222-22i−2i−2i2i0000000000000000000000000000
χ692-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i111-1-1-111-1-11−iii−ii−i−ii000000002-22i−2i−i3i33−3-111-1−iii−ii3−i3−i3i3i3−i3−333−3−330000000000000000
χ702-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i111-1-1-111-1-11−iii−ii−i−ii000000002-22i−2ii3−i3−33-111-1−iii−i−i3i3i3−i3−i3i33−3−333−30000000000000000
χ712-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i111-1-1-111-1-11−iii−ii−i−ii00000000-22−2i2i−i3i33−31-1-11i−i−iii3−i3i3−i3−i3i3−33−333−30000000000000000
χ722-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i111-1-1-111-1-11−iii−ii−i−ii00000000-22−2i2ii3−i3−331-1-11i−i−ii−i3i3−i3i3i3−i33−33−3−330000000000000000
χ732-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i000000002-2−2i2i−i3i3−33-111-1i−i−iii3−i3−i3i3i3−i33−3−333−30000000000000000
χ742-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i000000002-2−2i2ii3−i33−3-111-1i−i−ii−i3i3i3−i3−i3i3−333−3−330000000000000000
χ752-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i00000000-222i−2i−i3i3−331-1-11−iii−ii3−i3i3−i3−i3i33−33−3−330000000000000000
χ762-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i00000000-222i−2ii3−i33−31-1-11−iii−i−i3i3−i3i3i3−i3−33−333−30000000000000000
χ774444-4-444-4-4-244-4-444-4-4-22222-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-4-444-4-4-2-4-444-4-444-22222-2-2-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-244-4-4-4-444-22222-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-44444-4-4-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-44-44-44-44-4-24i−4i4i−4i4i−4i4i−4i2-2-222-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ824-44-44-44-44-4-2−4i4i−4i4i−4i4i−4i4i2-2-222-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-44-44-4-44-44-24i−4i4i−4i−4i4i−4i4i2-2-222-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ844-44-44-4-44-44-2−4i4i−4i4i4i−4i4i−4i2-2-222-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-800000080000000080000-8-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-4−4i34i3−4i34i3440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-44i3−4i34i3−4i3440000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-80000-880000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-40000000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000000

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