Finite Group Databasebeta

← Group #10863283

Character table — Group #10863283

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444444444881212121212121212121224242424242424242244888826612124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-2000000-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ2922-2-2-22-22222-2-2-2222-2-2-22i2i−2i−2i0000002-200002-200000000000002i2i−2i−2i00000000000000002i2i−2i−2i00000000002-2000
χ3022-2-2-22-22222-2-2-2222-2-2-22i2i−2i−2i0000002-200002-200000000000002i2i−2i−2i0000000000000000−2i−2i2i2i0000000000-22000
χ3122-2-2-22-22222-2-2-2222-2-2-2−2i−2i2i2i0000002-200002-20000000000000−2i−2i2i2i00000000000000002i2i−2i−2i0000000000-22000
χ3222-2-2-22-22222-2-2-2222-2-2-2−2i−2i2i2i0000002-200002-20000000000000−2i−2i2i2i0000000000000000−2i−2i2i2i00000000002-2000
χ332-222-22-2-222-2-22-22-2-222-22i−2i2i−2i000000220000-2-22i2i−2i−2i0000000002i−2i2i−2i000000000000002i−2i0000000002-200000000
χ342-222-22-2-222-2-22-22-2-222-22i−2i2i−2i000000220000-2-2−2i−2i2i2i0000000002i−2i2i−2i00000000000000−2i2i000000000-2200000000
χ352-222-22-2-222-2-22-22-2-222-2−2i2i−2i2i000000220000-2-22i2i−2i−2i000000000−2i2i−2i2i000000000000002i−2i000000000-2200000000
χ362-222-22-2-222-2-22-22-2-222-2−2i2i−2i2i000000220000-2-2−2i−2i2i2i000000000−2i2i−2i2i00000000000000−2i2i0000000002-200000000
χ372-222-22-2-22-222-2-22-2-222-20000000000-2-20000222i2i−2i−2i02-2000000000022-2-20000000000−2i2i0000000000002i−2i00000
χ382-222-22-2-22-222-2-22-2-222-20000000000-2-20000222i2i−2i−2i0-220000000000-2-2220000000000−2i2i000000000000−2i2i00000
χ392-222-22-2-22-222-2-22-2-222-20000000000-2-2000022−2i−2i2i2i02-2000000000022-2-200000000002i−2i000000000000−2i2i00000
χ402-222-22-2-22-222-2-22-2-222-20000000000-2-2000022−2i−2i2i2i0-220000000000-2-22200000000002i−2i0000000000002i−2i00000
χ412-22-22-2-22200002-22-22-2-200002-2−i2−i2i2i20022-2-2002-22-200000−i2i20000000000−i2−i2i2i2−i2−i2i2i22-200−i2i2−i2i2000000000000−i2i20
χ422-22-22-2-22200002-22-22-2-200002-2−i2−i2i2i20022-2-200-22-2200000−i2i20000000000−i2−i2i2i2−i2−i2i2i2-2200i2−i2i2−i2000000000000i2−i20
χ432-22-22-2-22200002-22-22-2-200002-2i2i2−i2−i20022-2-2002-22-200000i2−i20000000000i2i2−i2−i2i2i2−i2−i22-200i2−i2i2−i2000000000000i2−i20
χ442-22-22-2-22200002-22-22-2-200002-2i2i2−i2−i20022-2-200-22-2200000i2−i20000000000i2i2−i2−i2i2i2−i2−i2-2200−i2i2−i2i2000000000000−i2i20
χ452-22-22-2-22200002-22-22-2-20000-22−i2−i2i2i200-2-222002-22-200000i2−i20000000000−i2−i2i2i2i2i2−i2−i2-2200−i2i2−i2i2000000000000i2−i20
χ462-22-22-2-22200002-22-22-2-20000-22−i2−i2i2i200-2-22200-22-2200000i2−i20000000000−i2−i2i2i2i2i2−i2−i22-200i2−i2i2−i2000000000000−i2i20
χ472-22-22-2-22200002-22-22-2-20000-22i2i2−i2−i200-2-222002-22-200000−i2i20000000000i2i2−i2−i2−i2−i2i2i2-2200i2−i2i2−i2000000000000−i2i20
χ482-22-22-2-22200002-22-22-2-20000-22i2i2−i2−i200-2-22200-22-2200000−i2i20000000000i2i2−i2−i2−i2−i2i2i22-200−i2i2−i2i2000000000000i2−i20
χ492-2-2-2222-222-22-222-2-2-2-222-2-22002i−2i2i−2i2-20000-2200000002i−2i00002-2-2200002i−2i2i−2i0000000000000002i−2i0000000000
χ502-2-2-2222-222-22-222-2-2-2-222-2-2200−2i2i−2i2i2-20000-220000000−2i2i00002-2-220000−2i2i−2i2i000000000000000−2i2i0000000000
χ512-2-2-2222-222-22-222-2-2-2-22-222-2002i−2i2i−2i2-20000-220000000−2i2i0000-222-200002i−2i2i−2i000000000000000−2i2i0000000000
χ522-2-2-2222-222-22-222-2-2-2-22-222-200−2i2i−2i2i2-20000-2200000002i−2i0000-222-20000−2i2i−2i2i0000000000000002i−2i0000000000
χ532-2-2-2222-2-12-22-2-1-11111-12-2-22002i−2i2i−2i-113−33−31-100000002i−2i003−3-111-13−33−3−ii−ii−i3i3−i3i3000000000−i3i3−ii0000000000
χ542-2-2-2222-2-12-22-2-1-11111-12-2-22002i−2i2i−2i-11−33−331-100000002i−2i00−33-111-1−33−33−ii−iii3−i3i3−i3000000000i3−i3−ii0000000000
χ552-2-2-2222-2-12-22-2-1-11111-12-2-2200−2i2i−2i2i-113−33−31-10000000−2i2i003−3-111-13−33−3i−ii−ii3−i3i3−i3000000000i3−i3i−i0000000000
χ562-2-2-2222-2-12-22-2-1-11111-12-2-2200−2i2i−2i2i-11−33−331-10000000−2i2i00−33-111-1−33−33i−ii−i−i3i3−i3i3000000000−i3i3i−i0000000000
χ572-2-2-2222-2-12-22-2-1-11111-1-222-2002i−2i2i−2i-113−33−31-10000000−2i2i003−31-1-11−33−33−ii−ii−i3i3−i3i3000000000i3−i3i−i0000000000
χ582-2-2-2222-2-12-22-2-1-11111-1-222-2002i−2i2i−2i-11−33−331-10000000−2i2i00−331-1-113−33−3−ii−iii3−i3i3−i3000000000−i3i3i−i0000000000
χ592-2-2-2222-2-12-22-2-1-11111-1-222-200−2i2i−2i2i-113−33−31-100000002i−2i003−31-1-11−33−33i−ii−ii3−i3i3−i3000000000−i3i3−ii0000000000
χ602-2-2-2222-2-12-22-2-1-11111-1-222-200−2i2i−2i2i-11−33−331-100000002i−2i00−331-1-113−33−3i−ii−i−i3i3−i3i3000000000i3−i3−ii0000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-400002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-4-44-440000-4-4-444-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ64444-4-4-44-440000-4-4-444-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6544-444-4-4-4400004-4-44-44-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6644-444-4-4-4400004-4-44-44-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6744-444-4-4-4-20000-222-22-2200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ6844-444-4-4-4-20000-222-22-2200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ6944-444-4-4-4-20000-222-22-22000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7044-444-4-4-4-20000-222-22-22000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ7144-4-4-44-444-4-444-4444-4-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ7244-4-4-44-44-244-4-42-2-2-22224i4i−4i−4i000000-220000-220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7344-4-4-44-44-244-4-42-2-2-2222−4i−4i4i4i000000-220000-2200000000000002i2i−2i−2i00000000000000000000000000000000000
χ7444-4-4-44-44-2-4-4442-2-2-222200000000002-200002-20000000000000000023−23−23230000000000000000000000000000000
χ7544-4-4-44-44-2-4-4442-2-2-222200000000002-200002-200000000000000000−232323−230000000000000000000000000000000
χ764-444-44-4-4-24-4-442-222-2-224i−4i4i−4i000000-2-20000220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ774-444-44-4-4-24-4-442-222-2-22−4i4i−4i4i000000-2-200002200000000000002i−2i2i−2i00000000000000000000000000000000000
χ784-444-44-4-4-2-444-42-222-2-220000000000220000-2-2000004-40000000000-2-2220000000000000000000000000000000
χ794-444-44-4-4-2-444-42-222-2-220000000000220000-2-200000-44000000000022-2-20000000000000000000000000000000
χ804-44-44-4-44-20000-22-22-22200004-4−2i2−2i22i22i200-2-22200000000000−2i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ814-44-44-4-44-20000-22-22-22200004-42i22i2−2i2−2i200-2-222000000000002i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ824-44-44-4-44-20000-22-22-2220000-44−2i2−2i22i22i20022-2-2000000000002i2−2i20000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ834-44-44-4-44-20000-22-22-2220000-442i22i2−2i2−2i20022-2-200000000000−2i22i20000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ844-4-44-4-44440000-4-44-4-44400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ854-4-44-4-44440000-4-44-4-444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ864-4-4-4444-44-44-4444-4-4-4-440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-2-44-44-2-22222-200000000002-223−2323−23-2200000000000−2323000000000000000000000000000000000000000
χ884-4-4-4444-4-2-44-44-2-22222-200000000002-2−2323−2323-220000000000023−23000000000000000000000000000000000000000
χ89888-8-8-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-8-888-4000044-444-4-40000000000000000000000000000000000000000000000000000000000000000000000

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