Finite Group Databasebeta

← Group #10896485

Character table — Group #10896485

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212124444444412121212121212121212121212121212121212121212121288888888242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111-1-1-1-111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ7111111111111111-1-1-1-111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ8111111111111111-1-1-1-111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ1011111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ1111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ1211111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ1311111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1
χ1611111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ17222222222-2-222222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-222222222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-222-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−30000000000000000
χ3022222222-1-2-222222222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-222-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−3330000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ37222-2-2-22-2222000022-2-2-2-2222-2-2-2-22222-2-2-2-22-20000000000000022-2-222-2-2000000000000000000000000000000000000002-22-2000000
χ38222-2-2-22-2222000022-2-2-2-2222-2-2-2-22222-2-2-2-22-20000000000000022-2-222-2-200000000000000000000000000000000000000-22-22000000
χ39222-2-2-22-22220000-2-222-2-2222-2-2-2-22222-2-2-2-2-2200000000000000-2-222-2-222000000000000000000000000000000000000002-2-22000000
χ40222-2-2-22-22220000-2-222-2-2222-2-2-2-22222-2-2-2-2-2200000000000000-2-222-2-22200000000000000000000000000000000000000-222-2000000
χ41222-2-2-22-22-2-2000022-2-222222-2-2-2-2-2-2-2-22222-220000000000000022-2-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i
χ42222-2-2-22-22-2-2000022-2-222222-2-2-2-2-2-2-2-22222-220000000000000022-2-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i
χ43222-2-2-22-22-2-20000-2-22222222-2-2-2-2-2-2-2-222222-200000000000000-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i
χ44222-2-2-22-22-2-20000-2-22222222-2-2-2-2-2-2-2-222222-200000000000000-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i
χ4522-22-2-2-2222-22i2i−2i−2i00002-22-2-222-2-222-2-222-2-2002i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000002i−2i00002-20000
χ4622-22-2-2-2222-22i2i−2i−2i00002-22-2-222-2-222-2-222-2-2002i−2i00002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000−2i2i0000-220000
χ4722-22-2-2-2222-2−2i−2i2i2i00002-22-2-222-2-222-2-222-2-200−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000002i−2i0000-220000
χ4822-22-2-2-2222-2−2i−2i2i2i00002-22-2-222-2-222-2-222-2-200−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000−2i2i00002-20000
χ4922-22-2-2-222-222i2i−2i−2i0000-222-2-222-2-2-2-222-2-22200−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000002-22i−2i000000000000
χ5022-22-2-2-222-222i2i−2i−2i0000-222-2-222-2-2-2-222-2-22200−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000-22−2i2i000000000000
χ5122-22-2-2-222-22−2i−2i2i2i0000-222-2-222-2-2-2-222-2-222002i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000002-2−2i2i000000000000
χ5222-22-2-2-222-22−2i−2i2i2i0000-222-2-222-2-2-2-222-2-222002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000-222i−2i000000000000
χ532-2-222-22-22002i−2i2i−2i2-22-200-22-22-22-2000000000000002i−2i2i−2i2i−2i00002-22-200002i2i−2i−2i00002−2−i2i22−2−i2i22−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ542-2-222-22-22002i−2i2i−2i2-22-200-22-22-22-2000000000000002i−2i2i−2i2i−2i00002-22-200002i2i−2i−2i0000−22i2−i2−22i2−i2−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ552-2-222-22-22002i−2i2i−2i-22-2200-22-22-22-200000000000000−2i2i2i−2i2i−2i0000-22-220000−2i−2i2i2i00002−2−i2i2−22i2−i22−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ562-2-222-22-22002i−2i2i−2i-22-2200-22-22-22-200000000000000−2i2i2i−2i2i−2i0000-22-220000−2i−2i2i2i0000−22i2−i22−2−i2i2−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ572-2-222-22-2200−2i2i−2i2i2-22-200-22-22-22-200000000000000−2i2i−2i2i−2i2i00002-22-20000−2i−2i2i2i00002−2i2−i22−2i2−i22−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ582-2-222-22-2200−2i2i−2i2i2-22-200-22-22-22-200000000000000−2i2i−2i2i−2i2i00002-22-20000−2i−2i2i2i0000−22−i2i2−22−i2i2−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ592-2-222-22-2200−2i2i−2i2i-22-2200-22-22-22-2000000000000002i−2i−2i2i−2i2i0000-22-2200002i2i−2i−2i00002−2i2−i2−22−i2i22−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ602-2-222-22-2200−2i2i−2i2i-22-2200-22-22-22-2000000000000002i−2i−2i2i−2i2i0000-22-2200002i2i−2i−2i0000−22−i2i22−2i2−i2−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ612-2-222-22-2-1002i−2i2i−2i2-22-2001-11-11-113−33−33−33−30000002i−2i−ii−ii−i3i3−i3i3-11-113−33−3−i−iii−i3−i3i3i32−2−i2i22−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ622-2-222-22-2-1002i−2i2i−2i2-22-2001-11-11-113−33−33−33−30000002i−2i−ii−ii−i3i3−i3i3-11-113−33−3−i−iii−i3−i3i3i3−22i2−i2−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ632-2-222-22-2-1002i−2i2i−2i2-22-2001-11-11-11−33−33−33−330000002i−2i−ii−iii3−i3i3−i3-11-11−33−33−i−iiii3i3−i3−i32−2−i2i22−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ642-2-222-22-2-1002i−2i2i−2i2-22-2001-11-11-11−33−33−33−330000002i−2i−ii−iii3−i3i3−i3-11-11−33−33−i−iiii3i3−i3−i3−22i2−i2−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ652-2-222-22-2-1002i−2i2i−2i-22-22001-11-11-113−33−33−33−3000000−2i2i−ii−ii−i3i3−i3i31-11-1−33−33ii−i−ii3i3−i3−i32−2−i2i2−22i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ662-2-222-22-2-1002i−2i2i−2i-22-22001-11-11-113−33−33−33−3000000−2i2i−ii−ii−i3i3−i3i31-11-1−33−33ii−i−ii3i3−i3−i3−22i2−i22−2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ672-2-222-22-2-1002i−2i2i−2i-22-22001-11-11-11−33−33−33−33000000−2i2i−ii−iii3−i3i3−i31-11-13−33−3ii−i−i−i3−i3i3i32−2−i2i2−22i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ682-2-222-22-2-1002i−2i2i−2i-22-22001-11-11-11−33−33−33−33000000−2i2i−ii−iii3−i3i3−i31-11-13−33−3ii−i−i−i3−i3i3i3−22i2−i22−2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ692-2-222-22-2-100−2i2i−2i2i2-22-2001-11-11-113−33−33−33−3000000−2i2ii−ii−ii3−i3i3−i3-11-113−33−3ii−i−ii3i3−i3−i32−2i2−i22−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ702-2-222-22-2-100−2i2i−2i2i2-22-2001-11-11-113−33−33−33−3000000−2i2ii−ii−ii3−i3i3−i3-11-113−33−3ii−i−ii3i3−i3−i3−22−i2i2−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.