Finite Group Databasebeta

← Group #10823080

Character table — Group #10823080

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466666666666121212121212121222224444666666668888121212121212121224242424242424242244888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ9111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ10111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ11111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ12111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ13111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1
χ14111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1-1-111
χ15111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11-11-111-1-1-1-111-1-111
χ16111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-11-11-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222-2-2-2-22-22222-2-2-22222222-2-2-2-2-2-2-22222-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ24222222-2-2-2-22-22222-2-2-22222222-2-2-2-2-2-2-22222-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ25222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-11111-1-1-11111-122-2-222-2-2-1-1-1-1111122-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ26222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-11111-1-1-11111-122-2-2-2-222-1-1-1-11111-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-11111-1-1-11111-1-2-22222-2-21111-1-1-1-1-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ28222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-11111-1-1-11111-1-2-222-2-2221111-1-1-1-122-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-222-2-22222-2-2-2-22-2-2-2-222222-2-222-222-2-2-200000000000000000000000000000000000022-2-2000000000000
χ302222-2-222-2-22222-2-2-2-22-2-2-2-222222-2-222-222-2-2-2000000000000000000000000000000000000-2-222000000000000
χ312222-2-222-2-22-2-2-22222-2-2-2-2-222222-2-2-2-22-2-222200000000000000002-22-20000000022-2-222-2-20000000000000000
χ322222-2-222-2-22-2-2-22222-2-2-2-2-222222-2-2-2-22-2-22220000000000000000-22-2200000000-2-222-2-2220000000000000000
χ332222-2-222-2-2-1-2-2-22222-21111-1-1-1-1-11111-111-1-1-100000000−i3−i3i3i3−i3−i3i3i32-22-2−i3−i3i3i3−i3−i3i3i3-1-111-1-1110000000000000000
χ342222-2-222-2-2-1-2-2-22222-21111-1-1-1-1-11111-111-1-1-100000000−i3−i3i3i3−i3−i3i3i3-22-22i3i3−i3−i3i3i3−i3−i311-1-111-1-10000000000000000
χ352222-2-222-2-2-1-2-2-22222-21111-1-1-1-1-11111-111-1-1-100000000i3i3−i3−i3i3i3−i3−i32-22-2i3i3−i3−i3i3i3−i3−i3-1-111-1-1110000000000000000
χ362222-2-222-2-2-1-2-2-22222-21111-1-1-1-1-11111-111-1-1-100000000i3i3−i3−i3i3i3−i3−i3-22-22−i3−i3i3i3−i3−i3i3i311-1-111-1-10000000000000000
χ372222-2-2-2-22222-2-222-2-22-2-2-2-2222-2-22222-2-2-222-20000000000000000000000000000000000002-2-22000000000000
χ382222-2-2-2-22222-2-222-2-22-2-2-2-2222-2-22222-2-2-222-2000000000000000000000000000000000000-222-2000000000000
χ392222-2-2-2-2222-222-2-222-2-2-2-2-2222-2-222-2-2222-2-2200000000000000002-2-220000000022-2-2-2-2220000000000000000
χ402222-2-2-2-2222-222-2-222-2-2-2-2-2222-2-222-2-2222-2-220000000000000000-222-200000000-2-22222-2-20000000000000000
χ412222-2-2-2-222-1-222-2-222-21111-1-1-111-1-111-1-1-111-100000000−i3−i3i3i3i3i3−i3−i32-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ422222-2-2-2-222-1-222-2-222-21111-1-1-111-1-111-1-1-111-100000000−i3−i3i3i3i3i3−i3−i3-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ432222-2-2-2-222-1-222-2-222-21111-1-1-111-1-111-1-1-111-100000000i3i3−i3−i3−i3−i3i3i32-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ442222-2-2-2-222-1-222-2-222-21111-1-1-111-1-111-1-1-111-100000000i3i3−i3−i3−i3−i3i3i3-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ452-2-222-22-22-2222-22-22-2-222-2-22-2-22-22-22-2-22-22-220000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-222-22-22-2222-22-22-2-222-2-22-2-22-22-22-2-22-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-222-22-22-22-2-22-22-22222-2-22-2-22-22-2-222-22-22-22-22-200002-22-22-22-2000000000000000000000000000000000000
χ482-2-222-22-22-22-2-22-22-22222-2-22-2-22-22-2-222-22-22-2-22-220000-22-22-22-22000000000000000000000000000000000000
χ492-2-222-22-22-2-1-2-22-22-222-1-111-111-11-111-1-11-11-112-22-20000-11-11-11-1100003−33−33−33−33−33−33−33−30000000000000000
χ502-2-222-22-22-2-1-2-22-22-222-1-111-111-11-111-1-11-11-112-22-20000-11-11-11-110000−33−33−33−33−33−33−33−330000000000000000
χ512-2-222-22-22-2-1-2-22-22-222-1-111-111-11-111-1-11-11-11-22-2200001-11-11-11-100003−33−33−33−3−33−33−33−330000000000000000
χ522-2-222-22-22-2-1-2-22-22-222-1-111-111-11-111-1-11-11-11-22-2200001-11-11-11-10000−33−33−33−333−33−33−33−30000000000000000
χ532-2-222-2-22-2222-22-222-2-222-2-22-2-2-22-222-2-2-22-2220000000000000000000000000000000000000000000000002i−2i−2i2i
χ542-2-222-2-22-2222-22-222-2-222-2-22-2-2-22-222-2-2-22-222000000000000000000000000000000000000000000000000−2i2i2i−2i
χ552-2-222-2-22-222-22-22-2-22222-2-22-2-2-22-22-2222-22-2-22-2-2200002-22-2-22-22000000000000000000000000000000000000
χ562-2-222-2-22-222-22-22-2-22222-2-22-2-2-22-22-2222-22-2-2-222-20000-22-222-22-2000000000000000000000000000000000000
χ572-2-222-2-22-22-1-22-22-2-222-1-111-1111-11-11-1-1-11-1112-2-220000-11-111-11-100003−33−3−33−333−33−3−33−330000000000000000
χ582-2-222-2-22-22-1-22-22-2-222-1-111-1111-11-11-1-1-11-1112-2-220000-11-111-11-10000−33−333−33−3−33−333−33−30000000000000000
χ592-2-222-2-22-22-1-22-22-2-222-1-111-1111-11-11-1-1-11-111-222-200001-11-1-11-1100003−33−3−33−33−33−333−33−30000000000000000
χ602-2-222-2-22-22-1-22-22-2-222-1-111-1111-11-11-1-1-11-111-222-200001-11-1-11-110000−33−333−33−33−33−3−33−330000000000000000
χ612-2-22-222-2-22222-2-22-22-2-2-2222-2-22-2-222-222-2-22-200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ622-2-22-222-2-22222-2-22-22-2-2-2222-2-22-2-222-222-2-22-20000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ632-2-22-222-2-222-2-222-22-22-2-2222-2-22-2-22-22-2-222-22000000000000000000000000000000000000000000002-22-20000
χ642-2-22-222-2-222-2-222-22-22-2-2222-2-22-2-22-22-2-222-2200000000000000000000000000000000000000000000-22-220000
χ652-2-22-222-2-22-122-2-22-22-211-1-1-111-111-1-11-1-111-1100002i−2i2i−2i−i3i3i3−i3−i3i3i3−i30000−iii−i−iii−i3−3−333−3−330000000000000000
χ662-2-22-222-2-22-122-2-22-22-211-1-1-111-111-1-11-1-111-1100002i−2i2i−2ii3−i3−i3i3i3−i3−i3i30000−iii−i−iii−i−333−3−333−30000000000000000
χ672-2-22-222-2-22-122-2-22-22-211-1-1-111-111-1-11-1-111-110000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i30000i−i−iii−i−ii−333−3−333−30000000000000000
χ682-2-22-222-2-22-122-2-22-22-211-1-1-111-111-1-11-1-111-110000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i30000i−i−iii−i−ii3−3−333−3−330000000000000000
χ692-2-22-22-222-222-222-2-22-2-2-2222-2-2-222-22-22-222-2-200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ702-2-22-22-222-222-222-2-22-2-2-2222-2-2-222-22-22-222-2-20000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ712-2-22-22-222-22-22-2-222-22-2-2222-2-2-222-2-22-22-2-222000000000000000000000000000000000000000000002-2-220000
χ722-2-22-22-222-22-22-2-222-22-2-2222-2-2-222-2-22-22-2-22200000000000000000000000000000000000000000000-222-20000
χ732-2-22-22-222-2-12-222-2-22-211-1-1-1111-1-11-11-11-1-11100002i−2i−2i2i−i3i3i3−i3i3−i3−i3i30000−iii−ii−i−ii3−3−33−333−30000000000000000
χ742-2-22-22-222-2-12-222-2-22-211-1-1-1111-1-11-11-11-1-11100002i−2i−2i2ii3−i3−i3i3−i3i3i3−i30000−iii−ii−i−ii−333−33−3−330000000000000000
χ752-2-22-22-222-2-12-222-2-22-211-1-1-1111-1-11-11-11-1-1110000−2i2i2i−2i−i3i3i3−i3i3−i3−i3i30000i−i−ii−iii−i−333−33−3−330000000000000000
χ762-2-22-22-222-2-12-222-2-22-211-1-1-1111-1-11-11-11-1-1110000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i30000i−i−ii−iii−i3−3−33−333−30000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-44444-4-4-4-2-2-2-2-2-2-22222222-2-2-2-220000000000000000000000000000000000000000000000000000
χ794444-4-444-4-4-2444-4-4-4-442222-2-2-2-2-222-2-22-2-22220000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-24-4-444-4-442222-2-2-222-2-2-2-2222-2-220000000000000000000000000000000000000000000000000000
χ814-4-444-44-44-4-244-44-44-4-4-2-222-222-22-22-222-22-22-20000000000000000000000000000000000000000000000000000
χ824-4-444-4-44-44-24-44-444-4-4-2-222-2222-22-2-2222-22-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-444-4-44-2-4-444-44-4422-2-2-222-222-22-222-2-22-20000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-44-4-444-4422-2-2-2222-2-222-22-222-2-20000000000000000000000000000000000000000000000000000
χ8588-8-80000008000000000000-88-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000−4i34i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004i3−4i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000000
χ888-88-80000008000000000000-8-880000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-400000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000

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