Finite Group Databasebeta

← Group #10868450

Character table — Group #10868450

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444444444444441212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-11-1-11-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-111-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111111-11111-1-1-1-1-1-1-1-1111-1-1-111
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11111-1-1-1-11111-1-1-1111-1-1
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-111
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-1-1-11111-1-1-1-1-111111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1111-1-1-1-111-1-1111-1-1-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1111-1-1-1-11111-1-1-1111-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-1-1-11111-1-111-1-1111-111-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-11111111-1-1-11111-1-1-1-111-1-1-11-1-111
χ17222222222-22222-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000002222000000000000000000-200-20000
χ18222222222-22222-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000-2-2-2-200000000000000000020020000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-20000000000000000000022-2-2000000000000000000-20020000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-200000000000000000000-2-222000000000000000000200-20000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-111-1-111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000000002211-1-111-1-1000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-1-1-11111000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-221111-1-1-1-1000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ2922-2-22-22-2222i2i−2i−2i-2-2222-2-2-2-222i−2i000000002i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000000002i2i−2i−2i00000000002-20000000000
χ3022-2-22-22-2222i2i−2i−2i-2-2222-2-2-2-222i−2i000000002i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000000000−2i−2i2i2i0000000000-220000000000
χ3122-2-22-22-222−2i−2i2i2i-2-2222-2-2-2-22−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000000002i2i−2i−2i0000000000-220000000000
χ3222-2-22-22-222−2i−2i2i2i-2-2222-2-2-2-22−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000000000−2i−2i2i2i00000000002-20000000000
χ3322-2-22-22-22-22i2i−2i−2i22-222-2-2-2-22−2i2i000000002i2i−2i−2i−2i−2i2i2i-22-2200000000000000002i−2i2-200000000002i−2i002-200000000000000
χ3422-2-22-22-22-22i2i−2i−2i22-222-2-2-2-22−2i2i000000002i2i−2i−2i−2i−2i2i2i-22-220000000000000000−2i2i-220000000000−2i2i00-2200000000000000
χ3522-2-22-22-22-2−2i−2i2i2i22-222-2-2-2-222i−2i00000000−2i−2i2i2i2i2i−2i−2i-22-2200000000000000002i−2i-2200000000002i−2i00-2200000000000000
χ3622-2-22-22-22-2−2i−2i2i2i22-222-2-2-2-222i−2i00000000−2i−2i2i2i2i2i−2i−2i-22-220000000000000000−2i2i2-20000000000−2i2i002-200000000000000
χ3722-2-22-22-2-1-22i2i−2i−2i22-2-1-11111-1−2i2i00000000−i−iiiii−i−i1-11-1−i3−i3−i3−i3i3i3i3i33333−3−3−3−32i−2i2-20000000000−ii3−3-11−i3i3000000000000
χ3822-2-22-22-2-1-22i2i−2i−2i22-2-1-11111-1−2i2i00000000−i−iiiii−i−i1-11-1−i3−i3−i3−i3i3i3i3i33333−3−3−3−3−2i2i-220000000000i−i−331-1i3−i3000000000000
χ3922-2-22-22-2-1-22i2i−2i−2i22-2-1-11111-1−2i2i00000000−i−iiiii−i−i1-11-1i3i3i3i3−i3−i3−i3−i3−3−3−3−333332i−2i2-20000000000−ii−33-11i3−i3000000000000
χ4022-2-22-22-2-1-22i2i−2i−2i22-2-1-11111-1−2i2i00000000−i−iiiii−i−i1-11-1i3i3i3i3−i3−i3−i3−i3−3−3−3−33333−2i2i-220000000000i−i3−31-1−i3i3000000000000
χ4122-2-22-22-2-1-2−2i−2i2i2i22-2-1-11111-12i−2i00000000ii−i−i−i−iii1-11-1−i3−i3−i3−i3i3i3i3i3−3−3−3−333332i−2i-220000000000−ii3−31-1i3−i3000000000000
χ4222-2-22-22-2-1-2−2i−2i2i2i22-2-1-11111-12i−2i00000000ii−i−i−i−iii1-11-1−i3−i3−i3−i3i3i3i3i3−3−3−3−33333−2i2i2-20000000000i−i−33-11−i3i3000000000000
χ4322-2-22-22-2-1-2−2i−2i2i2i22-2-1-11111-12i−2i00000000ii−i−i−i−iii1-11-1i3i3i3i3−i3−i3−i3−i33333−3−3−3−32i−2i-220000000000−ii−331-1−i3i3000000000000
χ4422-2-22-22-2-1-2−2i−2i2i2i22-2-1-11111-12i−2i00000000ii−i−i−i−iii1-11-1i3i3i3i3−i3−i3−i3−i33333−3−3−3−3−2i2i2-20000000000i−i3−3-11i3−i3000000000000
χ452-22-222-2-22200002-2-2-2-22-2-2220022-2-20000000000002-2-2222-2-222-2-200000000000000002i−2i2i−2i0000000000000002i−2i00000
χ462-22-222-2-22200002-2-2-2-22-2-2220022-2-20000000000002-2-2222-2-222-2-20000000000000000−2i2i−2i2i000000000000000−2i2i00000
χ472-22-222-2-22200002-2-2-2-22-2-22200-2-2220000000000002-2-22-2-222-2-22200000000000000002i−2i2i−2i000000000000000−2i2i00000
χ482-22-222-2-22200002-2-2-2-22-2-22200-2-2220000000000002-2-22-2-222-2-2220000000000000000−2i2i−2i2i0000000000000002i−2i00000
χ492-2-222-2-22220000-22-2-2-2-222-220000002i2i−2i−2i0000000022-2-2000000002i2i−2i−2i2i2i−2i−2i000000002-2-220000000000002i−2i00000000
χ502-2-222-2-22220000-22-2-2-2-222-220000002i2i−2i−2i0000000022-2-2000000002i2i−2i−2i2i2i−2i−2i00000000-222-2000000000000−2i2i00000000
χ512-2-222-2-22220000-22-2-2-2-222-22000000−2i−2i2i2i0000000022-2-200000000−2i−2i2i2i−2i−2i2i2i000000002-2-22000000000000−2i2i00000000
χ522-2-222-2-22220000-22-2-2-2-222-22000000−2i−2i2i2i0000000022-2-200000000−2i−2i2i2i−2i−2i2i2i00000000-222-20000000000002i−2i00000000
χ532-2-2-2-2222202-22-20002-222-2-2-2002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−200002i−2i2i−2i0000000000000000000000−i2i2−i2i2
χ542-2-2-2-2222202-22-20002-222-2-2-2002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−20000−2i2i−2i2i0000000000000000000000i2−i2i2−i2
χ552-2-2-2-2222202-22-20002-222-2-2-200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−2200002i−2i2i−2i0000000000000000000000i2−i2i2−i2
χ562-2-2-2-2222202-22-20002-222-2-2-200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−220000−2i2i−2i2i0000000000000000000000−i2i2−i2i2
χ572-2-2-2-222220-22-220002-222-2-2-2002−22−2−22−22-22-22000000002−22−22−22−2−22−22−22−2200002i−2i−2i2i0000000000000000000000i2−i2−i2i2
χ582-2-2-2-222220-22-220002-222-2-2-2002−22−2−22−22-22-22000000002−22−22−22−2−22−22−22−220000−2i2i2i−2i0000000000000000000000−i2i2i2−i2
χ592-2-2-2-222220-22-220002-222-2-2-200−22−222−22−2-22-2200000000−22−22−22−222−22−22−22−200002i−2i−2i2i0000000000000000000000−i2i2i2−i2
χ602-2-2-2-222220-22-220002-222-2-2-200−22−222−22−2-22-2200000000−22−22−22−222−22−22−22−20000−2i2i2i−2i0000000000000000000000i2−i2−i2i2
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244000000002222-2-2-2-2222200000000000000000000000000000000000000000000000000
χ63444-4-4-4-44400000000-44-44-44-4000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ64444-4-4-4-44400000000-44-44-44-40000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ65444-4-4-4-44-2000000002-22-22-22000000−2i22i22i2−2i2000023−2323−230000i6−i6−i6i6−i6i6i6−i6i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ66444-4-4-4-44-2000000002-22-22-22000000−2i22i22i2−2i20000−2323−23230000−i6i6i6−i6i6−i6−i6i6i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ67444-4-4-4-44-2000000002-22-22-220000002i2−2i2−2i22i2000023−2323−230000−i6i6i6−i6i6−i6−i6i6−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ68444-4-4-4-44-2000000002-22-22-220000002i2−2i2−2i22i20000−2323−23230000i6−i6−i6i6−i6i6i6−i6−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ6944-44-44-4-4400000000-444-44-4-40022−22−2222000000000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ7044-44-44-4-4400000000-444-44-4-400−222222−220000000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ7144-44-44-4-4-2000000002-2-22-2220022−22−222200000000−2i32i32i3−2i30000−222−2−222−2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ7244-44-44-4-4-2000000002-2-22-2220022−22−2222000000002i3−2i3−2i32i30000−222−2−222−2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ7344-44-44-4-4-2000000002-2-22-22200−222222−2200000000−2i32i32i3−2i300002−2−222−2−22−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ7444-44-44-4-4-2000000002-2-22-22200−222222−22000000002i3−2i3−2i32i300002−2−222−2−22i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ7544-4-44-44-4-244i4i−4i−4i-4-44-2-22222-24i−4i00000000−2i−2i2i2i−2i−2i2i2i-22-2200000000000000000000000000000000000000000000000000
χ7644-4-44-44-4-24−4i−4i4i4i-4-44-2-22222-2−4i4i000000002i2i−2i−2i2i2i−2i−2i-22-2200000000000000000000000000000000000000000000000000
χ774-444-4-44-4404i−4i−4i4i0004-4-4-444-400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ784-444-4-44-440−4i4i4i−4i0004-4-4-444-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ794-444-4-44-4-204i−4i−4i4i000-2222-2-220000000000−2i2i2i−2i00000000i6−i6i6−i6−i6i6−i6i6−66−666−66−60000000000000000000000000000000000
χ804-444-4-44-4-204i−4i−4i4i000-2222-2-220000000000−2i2i2i−2i00000000−i6i6−i6i6i6−i6i6−i66−66−6−66−660000000000000000000000000000000000
χ814-444-4-44-4-20−4i4i4i−4i000-2222-2-2200000000002i−2i−2i2i00000000i6−i6i6−i6−i6i6−i6i66−66−6−66−660000000000000000000000000000000000
χ824-444-4-44-4-20−4i4i4i−4i000-2222-2-2200000000002i−2i−2i2i00000000−i6i6−i6i6i6−i6i6−i6−66−666−66−60000000000000000000000000000000000
χ834-44-444-4-44-40000-444-4-44-4-444000000000000000000-444-400000000000000000000000000000000000000000000000000
χ844-44-444-4-4-2400004-4-422-222-2-20044-4-4000000000000-222-2-2-222-2-222000000000000000000000000000000000000000000
χ854-44-444-4-4-2400004-4-422-222-2-200-4-444000000000000-222-222-2-222-2-2000000000000000000000000000000000000000000
χ864-44-444-4-4-2-40000-44422-222-2-20000000000000000002-2-2200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000
χ874-44-444-4-4-2-40000-44422-222-2-20000000000000000002-2-22000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000
χ884-4-444-4-444-400004-44-4-4-444-44000000000000000000-4-44400000000000000000000000000000000000000000000000000
χ894-4-444-4-44-240000-44-4222-2-22-20000004i4i−4i−4i00000000-2-22200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ904-4-444-4-44-240000-44-4222-2-22-2000000−4i−4i4i4i00000000-2-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ914-4-444-4-44-2-400004-44222-2-22-200000000000000000022-2-2−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000000000000000
χ924-4-444-4-44-2-400004-44222-2-22-200000000000000000022-2-22i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000000000000000
χ934-4-4-4-4444-204-44-4000-22-2-22220022−2222−2222−2222−22-22-2200000000−22−22−22−22−22−22−22−220000000000000000000000000000000000
χ944-4-4-4-4444-204-44-4000-22-2-222200−2222−2222−2222−2222-22-22000000002−22−22−22−22−22−22−22−20000000000000000000000000000000000
χ954-4-4-4-4444-20-44-44000-22-2-22220022−2222−22−2222−22222-22-200000000−22−22−22−222−22−22−22−20000000000000000000000000000000000
χ964-4-4-4-4444-20-44-44000-22-2-222200−2222−222222−2222−222-22-2000000002−22−22−22−2−22−22−22−220000000000000000000000000000000000

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