Finite Group Databasebeta

← Group #10822718

Character table — Group #10822718

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666121212121212121266668888888812121212242424242424242424242424242424242244666688881212121224242424242424244444444444444444
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1111111
χ911111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1111111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1211111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ1411111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ1511111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1611111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000002-2-2222-2-20000-2-222000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000-222-2-2-222000022-2-2000000000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-21111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−33333−3−3−3−32-2-22-1-111000011-1-133−3−333−3−30000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−33333−3−3−3−3-222-211-1-10000-1-111−3−333−3−3330000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−33333−3−3−3−333332-2-22-1-111000011-1-1−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−33333−3−3−3−33333-222-211-1-10000-1-11133−3−333−3−30000000000000000
χ2722222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000022-2-222220000-2-2-2-2000000000000000000000000
χ2822222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-222-2-2-2-200002222000000000000000000000000
χ2922222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-22-2-1-11122-2-2-1-111-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-22-2211-1-1-2-22211-1-11111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-22-2-1-111-2-222-1-1111111-1-1-1-10000000000000000
χ3222222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-22-2211-1-122-2-211-1-1-1-1-1-111110000000000000000
χ3322222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111111100000000-1-1-1-13333−3−3−3−3−3−3−3−3333322-2-2-1-1-1-10000111133−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111111100000000-1-1-1-13333−3−3−3−3−3−3−3−33333-2-22211110000-1-1-1-1−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−3−3−333333333−3−3−3−322-2-2-1-1-1-100001111−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−3−3−333333333−3−3−3−3-2-22211110000-1-1-1-133−3−3−3−3330000000000000000
χ37222-2-2-22-222-2-222-222-2-22-222-2-2-2-2222-2-222-2-222-2-20000000022-2-200000000000000000000000000000000000000002i−2i2i−2i000000000000
χ38222-2-2-22-222-2-222-222-2-22-222-2-2-2-2222-2-222-2-222-2-20000000022-2-20000000000000000000000000000000000000000−2i2i−2i2i000000000000
χ39222-2-2-22-222-2-22-22-2-222-2222-2-2-2-22-2-222-2-22222-2-200000000-2-22200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ40222-2-2-22-222-2-22-22-2-222-2222-2-2-2-22-2-222-2-22222-2-200000000-2-2220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ41222-2-2-22-2-2-22222-2-2-2222-222-2-2-2-2222-2-222-2-2-2-22200000000-2-22200000000000000000000000000000000000000002i−2i−2i2i000000000000
χ42222-2-2-22-2-2-22222-2-2-2222-222-2-2-2-2222-2-222-2-2-2-22200000000-2-2220000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ43222-2-2-22-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-222-2-2220000000022-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ44222-2-2-22-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-222-2-2220000000022-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-2-222-22-22-22-22222-22-2-2-2-2-222-2-222222-2-2-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462-2-222-22-22-22-22222-22-2-2-2-2-222-2-222222-2-2-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472-2-222-22-22-22-22-2-2-22-2222-2-222-2-22-2-2-2-222222-22-200000000-22-220000000000000000000000002-22-200002-22-22-22-20000000000000000
χ482-2-222-22-22-22-22-2-2-22-2222-2-222-2-22-2-2-2-222222-22-200000000-22-22000000000000000000000000-22-220000-22-22-22-220000000000000000
χ492-2-222-22-22-22-2-1222-22-2-2-211-1-111-1-1-1-1-11111-11-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii−i−iii−i−iii0000−i3i3−i3i30000−i3i3−i3i33−3−333−3−330000000000000000
χ502-2-222-22-22-22-2-1222-22-2-2-211-1-111-1-1-1-1-11111-11-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii−i−iii−i−iii0000i3−i3i3−i30000i3−i3i3−i3−333−3−333−30000000000000000
χ512-2-222-22-22-22-2-1222-22-2-2-211-1-111-1-1-1-1-11111-11-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−iii−i−iii−i−i0000−i3i3−i3i30000−i3i3−i3i3−333−3−333−30000000000000000
χ522-2-222-22-22-22-2-1222-22-2-2-211-1-111-1-1-1-1-11111-11-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−iii−i−iii−i−i0000i3−i3i3−i30000i3−i3i3−i33−3−333−3−330000000000000000
χ532-2-222-22-22-22-2-1-2-2-22-222211-1-111-11111-1-1-1-1-11-11000000001-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000−i3i3i3−i32-22-2i3−i3−i3i3-11-11-11-110000000000000000
χ542-2-222-22-22-22-2-1-2-2-22-222211-1-111-11111-1-1-1-1-11-11000000001-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000i3−i3−i3i3-22-22−i3i3i3−i31-11-11-11-10000000000000000
χ552-2-222-22-22-22-2-1-2-2-22-222211-1-111-11111-1-1-1-1-11-11000000001-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−i3i3i3−i3-22-22i3−i3−i3i31-11-11-11-10000000000000000
χ562-2-222-22-22-22-2-1-2-2-22-222211-1-111-11111-1-1-1-1-11-11000000001-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000i3−i3−i3i32-22-2−i3i3i3−i3-11-11-11-110000000000000000
χ572-2-222-22-2-22-22222-22-22-2-2-2-222-2-222222-2-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ582-2-222-22-2-22-22222-22-22-2-2-2-222-2-222222-2-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ592-2-222-22-2-22-222-2-22-22-222-2-222-2-22-2-2-2-22222-22-22000000002-22-20000000000000000000000002-2-2200002-22-2-22-220000000000000000
χ602-2-222-22-2-22-222-2-22-22-222-2-222-2-22-2-2-2-22222-22-22000000002-22-2000000000000000000000000-222-20000-22-222-22-20000000000000000
χ612-2-222-22-2-22-22-122-22-22-2-211-1-111-1-1-1-1-111111-11-12i2i−2i−2i−2i−2i2i2i1-11-1−i−iii−i−iiiii−i−iii−i−i0000−i3i3i3−i30000−i3i3i3−i33−3−33−333−30000000000000000
χ622-2-222-22-2-22-22-122-22-22-2-211-1-111-1-1-1-1-111111-11-12i2i−2i−2i−2i−2i2i2i1-11-1−i−iii−i−iiiii−i−iii−i−i0000i3−i3−i3i30000i3−i3−i3i3−333−33−3−330000000000000000
χ632-2-222-22-2-22-22-122-22-22-2-211-1-111-1-1-1-1-111111-11-1−2i−2i2i2i2i2i−2i−2i1-11-1ii−i−iii−i−i−i−iii−i−iii0000−i3i3i3−i30000−i3i3i3−i3−333−33−3−330000000000000000
χ642-2-222-22-2-22-22-122-22-22-2-211-1-111-1-1-1-1-111111-11-1−2i−2i2i2i2i2i−2i−2i1-11-1ii−i−iii−i−i−i−iii−i−iii0000i3−i3−i3i30000i3−i3−i3i33−3−33−333−30000000000000000
χ652-2-222-22-2-22-22-1-2-22-22-22211-1-111-11111-1-1-1-11-11-100000000-11-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3i3−i3i32-2-22i3−i3i3−i3-11-111-11-10000000000000000
χ662-2-222-22-2-22-22-1-2-22-22-22211-1-111-11111-1-1-1-11-11-100000000-11-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3−i3i3−i3-222-2−i3i3−i3i31-11-1-11-110000000000000000
χ672-2-222-22-2-22-22-1-2-22-22-22211-1-111-11111-1-1-1-11-11-100000000-11-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−i3i3−i3i3-222-2i3−i3i3−i31-11-1-11-110000000000000000
χ682-2-222-22-2-22-22-1-2-22-22-22211-1-111-11111-1-1-1-11-11-100000000-11-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000i3−i3i3−i32-2-22−i3i3−i3i3-11-111-11-10000000000000000
χ692-2-2-2-22222-2-2222-22-2-22-22-2-2-2-222222-2-2-2-2222-2-22000000002-2-22000000000000000000000000000000000000000000002-200002-20000
χ702-2-2-2-22222-2-2222-22-2-22-22-2-2-2-222222-2-2-2-2222-2-22000000002-2-2200000000000000000000000000000000000000000000-220000-220000
χ712-2-2-2-22222-2-222-22-222-22-2-2-2-2-2222-2-22222-2-22-2-2200000000-222-200000000000000000000000000000000000000000000002-22-2000000
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χ8844-4-44-4-4400004000000004-4-44-44-40000000000002i2−2i22i2−2i2000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ8944-4-44-4-440000-200000000-222-22-2223−23−232323−23−23230000−2i22i2−2i22i2000000002ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000000000000000
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χ9144-4-44-4-440000-200000000-222-22-22−232323−23−232323−230000−2i22i2−2i22i2000000002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000000000
χ9244-4-44-4-440000-200000000-222-22-22−232323−23−232323−2300002i2−2i22i2−2i200000000−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000000000000000
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χ944-444-4-4-440000400000000-444-4-44-400000000000000002i2−2i2−2i22i20000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
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χ974-444-4-4-440000-2000000002-2-222-22−2323−232323−2323−2300000000−2i22i22i2−2i20000000000002ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000000000000000
χ984-444-4-4-440000-2000000002-2-222-22−2323−232323−2323−23000000002i2−2i2−2i22i2000000000000−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000000000000000
χ994-44-444-4-40000400000000-44-444-4-400000000000022−22−22220000000022−22−222222−22−2222000000000000000000000000000000000000000000000000
χ1004-44-444-4-40000400000000-44-444-4-4000000000000−222222−2200000000−222222−22−222222−22000000000000000000000000000000000000000000000000
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χ1044-44-444-4-40000-2000000002-22-2-222−232323−2323−23−23230000−222222−2200000000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000000000000000
χ1054-4-4-4-44444-4-44-24-44-4-44-442222-2-2-2-2-22222-2-2-222-200000000-222-200000000000000000000000000000000000000000000000000000000
χ1064-4-4-4-44444-4-44-2-44-444-44-42222-2-2-222-2-2-2-222-222-2000000002-2-2200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-4444-444-4-24-4-444-4-442222-2-2-2-2-22222-2-22-2-22000000002-2-2200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4-4444-444-4-2-444-4-444-42222-2-2-222-2-2-2-2222-2-2200000000-222-200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.