Finite Group Databasebeta

← Group #10823078

Character table — Group #10823078

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466612121212666666121212121212224466668888888812121212242424242424242424242424242424242222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ12111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ13111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ14111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ15111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ27222222-2-2-2-22-22222-2-2-2222-2-2-2-222-2-2-2-2-2-222220000000000002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ28222222-2-2-2-22-22222-2-2-2222-2-2-2-222-2-2-2-2-2-22222000000000000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-1-11111-1-111112-22-2-1-11122-2-222-2-2-1-111-1-1-1-11111-1-1-1-111110000000000000000
χ30222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-1-11111-1-111112-22-2-1-111-2-222-2-222-1-1111111-1-1-1-11111-1-1-1-10000000000000000
χ31222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-1-11111-1-11111-22-2211-1-122-2-2-2-22211-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ32222222-2-2-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-1-11111-1-11111-22-2211-1-1-2-22222-2-211-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ33222222-2-2-2-2-1-22222-2-2-2-1-1-11111-1-1111111-1-1-1-10000−i3i3i3−i300002i−2i−2i2i−i3i3i3−i333−3−3−3−333−i−iiiii−i−i0000000000000000
χ34222222-2-2-2-2-1-22222-2-2-2-1-1-11111-1-1111111-1-1-1-10000−i3i3i3−i30000−2i2i2i−2i−i3i3i3−i3−3−33333−3−3ii−i−i−i−iii0000000000000000
χ35222222-2-2-2-2-1-22222-2-2-2-1-1-11111-1-1111111-1-1-1-10000i3−i3−i3i300002i−2i−2i2ii3−i3−i3i3−3−33333−3−3−i−iiiii−i−i0000000000000000
χ36222222-2-2-2-2-1-22222-2-2-2-1-1-11111-1-1111111-1-1-1-10000i3−i3−i3i30000−2i2i2i−2ii3−i3−i3i333−3−3−3−333ii−i−i−i−iii0000000000000000
χ372222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-222-2-2222200000000-2-2-2-200000000000000000000000000000000
χ382222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-200000000222200000000000000000000000000000000
χ392222-2-222-2-22-2-2-22222-22222222-2-222-2-2-2-2-2-222000000002-22-2000000002-22-22-22-2000000000000000000000000
χ402222-2-222-2-22-2-2-22222-22222222-2-222-2-2-2-2-2-22200000000-22-2200000000-22-22-22-22000000000000000000000000
χ412222-2-222-2-2-1222-2-2-2-22-1-1-1111111-1-111-1-1-1-11122-2-2-1-1-1-10000000011113−3−333−3−333−33−33−33−30000000000000000
χ422222-2-222-2-2-1222-2-2-2-22-1-1-1111111-1-111-1-1-1-11122-2-2-1-1-1-1000000001111−333−3−333−3−33−33−33−330000000000000000
χ432222-2-222-2-2-1222-2-2-2-22-1-1-1111111-1-111-1-1-1-111-2-222111100000000-1-1-1-13−3−333−3−33−33−33−33−330000000000000000
χ442222-2-222-2-2-1222-2-2-2-22-1-1-1111111-1-111-1-1-1-111-2-222111100000000-1-1-1-1−333−3−333−33−33−33−33−30000000000000000
χ452222-2-222-2-2-1-2-2-22222-2-1-1-1-1-1-1-111-1-1111111-1-10000−i3i3−i3i32-22-20000i3−i3i3−i3-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ462222-2-222-2-2-1-2-2-22222-2-1-1-1-1-1-1-111-1-1111111-1-10000−i3i3−i3i3-22-220000i3−i3i3−i31-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ472222-2-222-2-2-1-2-2-22222-2-1-1-1-1-1-1-111-1-1111111-1-10000i3−i3i3−i32-22-20000−i3i3−i3i3-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ482222-2-222-2-2-1-2-2-22222-2-1-1-1-1-1-1-111-1-1111111-1-10000i3−i3i3−i3-22-220000−i3i3−i3i31-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ492222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2222-2-2222-2-200000000-2-22200000000000000000000000000000000
χ502222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-222-222-2-2-2220000000022-2-200000000000000000000000000000000
χ512222-2-2-2-2222-222-2-222-22222222-2-2-2-222-2-222-2-2000000002-2-22000000002-22-2-22-22000000000000000000000000
χ522222-2-2-2-2222-222-2-222-22222222-2-2-2-222-2-222-2-200000000-222-200000000-22-222-22-2000000000000000000000000
χ532222-2-2-2-222-12-2-222-2-22-1-1-111111111-1-1-1-111-1-12-2-22-1-1110000000011-1-13−3−33−333−33−33−3−33−330000000000000000
χ542222-2-2-2-222-12-2-222-2-22-1-1-111111111-1-1-1-111-1-12-2-22-1-1110000000011-1-1−333−33−3−33−33−333−33−30000000000000000
χ552222-2-2-2-222-12-2-222-2-22-1-1-111111111-1-1-1-111-1-1-222-211-1-100000000-1-1113−3−33−333−3−33−333−33−30000000000000000
χ562222-2-2-2-222-12-2-222-2-22-1-1-111111111-1-1-1-111-1-1-222-211-1-100000000-1-111−333−33−3−333−33−3−33−330000000000000000
χ572222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-11111-1-111-1-1110000−i3i3i3−i32-2-220000i3−i3−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ582222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-11111-1-111-1-1110000−i3i3i3−i3-222-20000i3−i3−i3i31-11-1-11-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ592222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-11111-1-111-1-1110000i3−i3−i3i32-2-220000−i3i3i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-11111-1-111-1-1110000i3−i3−i3i3-222-20000−i3i3i3−i31-11-1-11-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ6122-2-22-22-22-2222-22-22-2-2-2-2222-2-22-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ6222-2-22-22-22-2222-22-22-2-2-2-2222-2-22-22-22-22-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ6322-2-22-22-22-22-2-22-22-222-2-22-2-2222-22-22-2-22-22-220000000000000000000000000000000000002-22-2000000000000
χ6422-2-22-22-22-22-2-22-22-222-2-22-2-2222-22-22-2-22-22-22000000000000000000000000000000000000-22-22000000000000
χ6522-2-22-2-22-2222-22-222-2-2-2-2222-2-22-2-22-222-2-22-220000000000000000000000000000000000000000000000002i−2i−2i2i
χ6622-2-22-2-22-2222-22-222-2-2-2-2222-2-22-2-22-222-2-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i
χ6722-2-22-2-22-222-22-22-2-222-2-22-2-2222-2-22-22-222-22-20000000000000000000000000000000000002-2-22000000000000
χ6822-2-22-2-22-222-22-22-2-222-2-22-2-2222-2-22-22-222-22-2000000000000000000000000000000000000-222-2000000000000
χ6922-2-2-222-2-22222-2-22-22-2-2-22-2-222-222-2-222-22-2-2200000000000000000000000000000000000000002i−2i2i−2i00000000
χ7022-2-2-222-2-22222-2-22-22-2-2-22-2-222-222-2-222-22-2-220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7122-2-2-222-2-222-2-222-22-22-2-2222-2-2-222-2-22-22-222-2000000000000000000000000000000000000000000002-22-20000
χ7222-2-2-222-2-222-2-222-22-22-2-2222-2-2-222-2-22-22-222-200000000000000000000000000000000000000000000-22-220000
χ7322-2-2-22-222-222-222-2-22-2-2-22-2-222-22-222-22-2-222-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7422-2-2-22-222-222-222-2-22-2-2-22-2-222-22-222-22-2-222-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7522-2-2-22-222-22-22-2-222-22-2-2222-2-2-22-222-2-222-2-22000000000000000000000000000000000000000000002-2-220000
χ7622-2-2-22-222-22-22-2-222-22-2-2222-2-2-22-222-2-222-2-2200000000000000000000000000000000000000000000-222-20000
χ7744-4-44-44-44-4-244-44-44-4-422-2-2-222-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ7844-4-44-44-44-4-2-4-44-44-44422-222-2-2-22-22-222-22-22-20000000000000000000000000000000000000000000000000000
χ7944-4-44-4-44-44-24-44-444-4-422-2-2-222-222-22-2-222-22-20000000000000000000000000000000000000000000000000000
χ8044-4-44-4-44-44-2-44-44-4-44422-222-2-2-222-22-22-2-22-220000000000000000000000000000000000000000000000000000
χ8144-4-4-444-4-44-244-4-44-44-422-222-2-22-2-222-2-22-222-20000000000000000000000000000000000000000000000000000
χ8244-4-4-444-4-44-2-4-444-44-4422-2-2-2222-2-222-22-22-2-220000000000000000000000000000000000000000000000000000
χ8344-4-4-44-444-4-24-444-4-44-422-222-2-22-22-2-22-222-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-44-444-4-2-44-4-444-4422-2-2-2222-22-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ858-88-80000008000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000-44443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-400000000-444−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000

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