Finite Group Databasebeta

← Group #11713009

Character table — Group #11713009

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222224444333366666612121212666612121212121224242424666612121212121224242424888816161616161632323232
order124424888888882244248888888822442488888888444444888888883612126122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ3111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ4111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ511-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i
χ611-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii
χ711-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii
χ811-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i
χ92222-2-2000000002222-2-2000000002222-2-2000000002222-2-2000000002222-2-200000000
χ1022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-200000000
χ112-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000
χ122-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000
χ132-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000
χ142-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ17111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1
χ18111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111
χ1911-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii11-1-1-1111-1-1i−ii−i
χ2011-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i11-1-1-1111-1-1−ii−ii
χ2111-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i11-1-1-11-1-111i−i−ii
χ2211-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii11-1-1-11-1-111−iii−i
χ232222-2-2000000002222-2-200000000-2-2-2-22200000000-2-2-2-222000000002222-2-200000000
χ2422-2-22-20000000022-2-22-200000000-2-222-2200000000-2-222-220000000022-2-22-200000000
χ252-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−2200002-22i−2i00i2−i22−20000
χ262-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−200002-22i−2i00−i2i2−220000
χ272-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−20000-222i−2i00−i2i22−200002-2−2i2i00i2−i2−220000
χ282-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−220000-222i−2i00i2−i2−2200002-2−2i2i00−i2i22−20000
χ2922222222222222222222222222220000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ302222222222-2-2-2-22222222222-2-2-2-20000000000000000000000000000-1-1-1-1-1-1-1-1-1-11111
χ31222222-2-2-2-222-2-2222222-2-2-2-222-2-20000000000000000000000000000-1-1-1-1-1-11111-1-111
χ32222222-2-2-2-2-2-222222222-2-2-2-2-2-2220000000000000000000000000000-1-1-1-1-1-1111111-1-1
χ3322-2-2-2222-2-22i−2i2i−2i22-2-2-2222-2-22i−2i2i−2i0000000000000000000000000000-1-1111-1-1-111−ii−ii
χ3422-2-2-2222-2-2−2i2i−2i2i22-2-2-2222-2-2−2i2i−2i2i0000000000000000000000000000-1-1111-1-1-111i−ii−i
χ3522-2-2-22-2-2222i−2i−2i2i22-2-2-22-2-2222i−2i−2i2i0000000000000000000000000000-1-1111-111-1-1−iii−i
χ3622-2-2-22-2-222−2i2i2i−2i22-2-2-22-2-222−2i2i2i−2i0000000000000000000000000000-1-1111-111-1-1i−i−ii
χ374444-4-4000000004444-4-4000000000000000000000000000000000000-2-2-2-22200000000
χ3844-4-44-40000000044-4-44-4000000000000000000000000000000000000-2-222-2200000000
χ394-44i−4i002i2−2i222−2200004-44i−4i002i2−2i222−2200000000000000000000000000000000-22−2i2i00−i2i2−220000
χ404-44i−4i00−2i22i2−222200004-44i−4i00−2i22i2−222200000000000000000000000000000000-22−2i2i00i2−i22−20000
χ414-4−4i4i002i2−2i2−222200004-4−4i4i002i2−2i2−222200000000000000000000000000000000-222i−2i00−i2i22−20000
χ424-4−4i4i00−2i22i222−2200004-4−4i4i00−2i22i222−2200000000000000000000000000000000-222i−2i00i2−i2−220000
χ4333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ443333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000
χ45333333-3-3-3-333-3-3-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11100000000000000
χ46333333-3-3-3-3-3-333-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-100000000000000
χ4733-3-3-3333-3-33i−3i3i−3i-1-1111-1-1-111−ii−ii11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii00000000000000
χ4833-3-3-3333-3-3−3i3i−3i3i-1-1111-1-1-111i−ii−i11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i00000000000000
χ4933-3-3-33-3-3333i−3i−3i3i-1-1111-111-1-1−iii−i11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i00000000000000
χ5033-3-3-33-3-333−3i3i3i−3i-1-1111-111-1-1i−i−ii11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii00000000000000
χ516666-6-600000000-2-2-2-222000000002222-2-200000000-2-2-2-2220000000000000000000000
χ5266-6-66-600000000-2-222-220000000022-2-22-200000000-2-222-220000000000000000000000
χ536-66i−6i003i2−3i232−320000-22−2i2i00−i2i2−2200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−22000000000000000000
χ546-66i−6i00−3i23i2−32320000-22−2i2i00i2−i22−200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−2000000000000000000
χ556-6−6i6i003i2−3i2−32320000-222i−2i00−i2i22−200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−2000000000000000000
χ566-6−6i6i00−3i23i232−320000-222i−2i00i2−i2−2200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−22000000000000000000
χ5733333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111100000000000000
χ583333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-100000000000000
χ59333333-3-3-3-333-3-3-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-100000000000000
χ60333333-3-3-3-3-3-333-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-11100000000000000
χ6133-3-3-3333-3-33i−3i3i−3i-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii11-1-1-1111-1-1i−ii−i00000000000000
χ6233-3-3-3333-3-3−3i3i−3i3i-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i11-1-1-1111-1-1−ii−ii00000000000000
χ6333-3-3-33-3-3333i−3i−3i3i-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i11-1-1-11-1-111i−i−ii00000000000000
χ6433-3-3-33-3-333−3i3i3i−3i-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii11-1-1-11-1-111−iii−i00000000000000
χ656666-6-600000000-2-2-2-22200000000-2-2-2-222000000002222-2-20000000000000000000000
χ6666-6-66-600000000-2-222-2200000000-2-222-220000000022-2-22-20000000000000000000000
χ676-66i−6i003i2−3i232−320000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−2200002-22i−2i00i2−i22−2000000000000000000
χ686-66i−6i00−3i23i2−32320000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−200002-22i−2i00−i2i2−22000000000000000000
χ696-6−6i6i003i2−3i2−32320000-222i−2i00−i2i22−20000-222i−2i00−i2i22−200002-2−2i2i00i2−i2−22000000000000000000
χ706-6−6i6i00−3i23i232−320000-222i−2i00i2−i2−220000-222i−2i00i2−i2−2200002-2−2i2i00−i2i22−2000000000000000000

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