Finite Group Databasebeta

← Group #10868456

Character table — Group #10868456

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122244444882
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
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-11111-1-1-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111111-1-1-1-111-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-111-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-11111-1-11-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-2222200-2000000000000-2-200000000-2-2220000000000000-200000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-200-2000000000000-2-20000000022-2-20000000000000200000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000000000002200000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2002000000000000220000000022220000000000000-200000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-22-2-22211111111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-211111111-1-111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-2-21111-1-1-1-111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-222221111-1-1-1-1111111-1-1-1-100000000-211-1-10000000000
χ2922-22-22-2-222-2-22-222-2-2-22002i2i−2i−2i00002-200002-22i2i−2i−2i00000002i2i−2i−2i000000000000002i−2i000000000002-200000000
χ3022-22-22-2-222-2-22-222-2-2-22002i2i−2i−2i00002-200002-2−2i−2i2i2i00000002i2i−2i−2i00000000000000−2i2i00000000000-2200000000
χ3122-22-22-2-222-2-22-222-2-2-2200−2i−2i2i2i00002-200002-22i2i−2i−2i0000000−2i−2i2i2i000000000000002i−2i00000000000-2200000000
χ3222-22-22-2-222-2-22-222-2-2-2200−2i−2i2i2i00002-200002-2−2i−2i2i2i0000000−2i−2i2i2i00000000000000−2i2i000000000002-200000000
χ3322-22-22-2-22-222-2-222-2-2-220000000000-220000-222i2i−2i−2i2i−2i0000000002i2i−2i−2i0000000000−2i2i00000000000002-2000000
χ3422-22-22-2-22-222-2-222-2-2-220000000000-220000-222i2i−2i−2i−2i2i000000000−2i−2i2i2i0000000000−2i2i0000000000000-22000000
χ3522-22-22-2-22-222-2-222-2-2-220000000000-220000-22−2i−2i2i2i2i−2i0000000002i2i−2i−2i00000000002i−2i0000000000000-22000000
χ3622-22-22-2-22-222-2-222-2-2-220000000000-220000-22−2i−2i2i2i−2i2i000000000−2i−2i2i2i00000000002i−2i00000000000002-2000000
χ372-2222-2-2-2200002-2-22-2-222i−2i0000−i2−i2i2i2002i2i−2i−2i002i−2i2i−2i000002−20000000000−i2−i2i2i222−2−2002-222−2−2000000000000−i2i20
χ382-2222-2-2-2200002-2-22-2-222i−2i0000−i2−i2i2i2002i2i−2i−2i00−2i2i−2i2i000002−20000000000−i2−i2i2i222−2−200-22−2−222000000000000i2−i20
χ392-2222-2-2-2200002-2-22-2-222i−2i0000i2i2−i2−i2002i2i−2i−2i002i−2i2i−2i00000−220000000000i2i2−i2−i2−2−222002-2−2−222000000000000i2−i20
χ402-2222-2-2-2200002-2-22-2-222i−2i0000i2i2−i2−i2002i2i−2i−2i00−2i2i−2i2i00000−220000000000i2i2−i2−i2−2−22200-2222−2−2000000000000−i2i20
χ412-2222-2-2-2200002-2-22-2-22−2i2i0000−i2−i2i2i200−2i−2i2i2i002i−2i2i−2i00000−220000000000−i2−i2i2i2−2−22200-2222−2−2000000000000i2−i20
χ422-2222-2-2-2200002-2-22-2-22−2i2i0000−i2−i2i2i200−2i−2i2i2i00−2i2i−2i2i00000−220000000000−i2−i2i2i2−2−222002-2−2−222000000000000−i2i20
χ432-2222-2-2-2200002-2-22-2-22−2i2i0000i2i2−i2−i200−2i−2i2i2i002i−2i2i−2i000002−20000000000i2i2−i2−i222−2−200-22−2−222000000000000−i2i20
χ442-2222-2-2-2200002-2-22-2-22−2i2i0000i2i2−i2−i200−2i−2i2i2i00−2i2i−2i2i000002−20000000000i2i2−i2−i222−2−2002-222−2−2000000000000i2−i20
χ452-22-2-222-2222-2-2-22-222-2-2002i−2i2i−2i2-22-22-20000-2200000002i−2i002i−2i2i−2i0000002-22-20000000000000002i−2i0000000000
χ462-22-2-222-2222-2-2-22-222-2-2002i−2i2i−2i-22-222-20000-220000000−2i2i002i−2i2i−2i000000-22-22000000000000000−2i2i0000000000
χ472-22-2-222-2222-2-2-22-222-2-200−2i2i−2i2i2-22-22-20000-220000000−2i2i00−2i2i−2i2i0000002-22-2000000000000000−2i2i0000000000
χ482-22-2-222-2222-2-2-22-222-2-200−2i2i−2i2i-22-222-20000-2200000002i−2i00−2i2i−2i2i000000-22-220000000000000002i−2i0000000000
χ492-22-2-222-2-122-2-21-11-1-111002i−2i2i−2i2-22-2-113−33−31-100000002i−2i00−ii−ii−i3i3−i3i33−3-11-113−33−3000000000−i3i3−ii0000000000
χ502-22-2-222-2-122-2-21-11-1-111002i−2i2i−2i2-22-2-11−33−331-100000002i−2i00−ii−iii3−i3i3−i3−33-11-11−33−33000000000i3−i3−ii0000000000
χ512-22-2-222-2-122-2-21-11-1-111002i−2i2i−2i-22-22-113−33−31-10000000−2i2i00−ii−ii−i3i3−i3i33−31-11-1−33−33000000000i3−i3i−i0000000000
χ522-22-2-222-2-122-2-21-11-1-111002i−2i2i−2i-22-22-11−33−331-10000000−2i2i00−ii−iii3−i3i3−i3−331-11-13−33−3000000000−i3i3i−i0000000000
χ532-22-2-222-2-122-2-21-11-1-11100−2i2i−2i2i2-22-2-113−33−31-10000000−2i2i00i−ii−ii3−i3i3−i33−3-11-113−33−3000000000i3−i3i−i0000000000
χ542-22-2-222-2-122-2-21-11-1-11100−2i2i−2i2i2-22-2-11−33−331-10000000−2i2i00i−ii−i−i3i3−i3i3−33-11-11−33−33000000000−i3i3i−i0000000000
χ552-22-2-222-2-122-2-21-11-1-11100−2i2i−2i2i-22-22-113−33−31-100000002i−2i00i−ii−ii3−i3i3−i33−31-11-1−33−33000000000−i3i3−ii0000000000
χ562-22-2-222-2-122-2-21-11-1-11100−2i2i−2i2i-22-22-11−33−331-100000002i−2i00i−ii−i−i3i3−i3i3−331-11-13−33−3000000000i3−i3−ii0000000000
χ572-2-2-222-2222-22-222-2-2-22-2002-2-220000220000-2-2000000000002-2-220000000000000000002i−2i2i−2i00000000002i−2i000
χ582-2-2-222-2222-22-222-2-2-22-2002-2-220000220000-2-2000000000002-2-22000000000000000000−2i2i−2i2i0000000000−2i2i000
χ592-2-2-222-2222-22-222-2-2-22-200-222-20000220000-2-200000000000-222-20000000000000000002i−2i2i−2i0000000000−2i2i000
χ602-2-2-222-2222-22-222-2-2-22-200-222-20000220000-2-200000000000-222-2000000000000000000−2i2i−2i2i00000000002i−2i000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-222000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400000000222222220000004000000000000-2-20000000000000000000000000000000
χ63444-4-4-4-4440000-4-444-44-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ64444-4-4-4-4440000-4-444-44-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ65444-4-4-4-44-2000022-2-22-22000000−2i22i22i2−2i200−2i32i32i3−2i300000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ66444-4-4-4-44-2000022-2-22-22000000−2i22i22i2−2i2002i3−2i3−2i32i300000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ67444-4-4-4-44-2000022-2-22-220000002i2−2i2−2i22i200−2i32i32i3−2i300000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ68444-4-4-4-44-2000022-2-22-220000002i2−2i2−2i22i2002i3−2i3−2i32i300000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ6944-44-44-4-4-24-4-442-2-2222-2004i4i−4i−4i0000-220000-2200000000000−2i−2i2i2i0000000000000000000000000000000000000
χ7044-44-44-4-4-24-4-442-2-2222-200−4i−4i4i4i0000-220000-22000000000002i2i−2i−2i0000000000000000000000000000000000000
χ7144-44-44-4-4-2-444-42-2-2222-200000000002-200002-200004i−4i000000000−2i−2i2i2i000000000000000000000000000000000
χ7244-44-44-4-4-2-444-42-2-2222-200000000002-200002-20000−4i4i0000000002i2i−2i−2i000000000000000000000000000000000
χ7344-4-44-44-4400004-44-44-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ7444-4-44-44-4400004-44-44-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ754-4444-4-4-4-20000-222-222-24i−4i0000−2i2−2i22i22i200−2i−2i2i2i0000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ764-4444-4-4-4-20000-222-222-24i−4i00002i22i2−2i2−2i200−2i−2i2i2i00000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ774-4444-4-4-4-20000-222-222-2−4i4i0000−2i2−2i22i22i2002i2i−2i−2i00000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ784-4444-4-4-4-20000-222-222-2−4i4i00002i22i2−2i2−2i2002i2i−2i−2i0000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ794-44-4-444-44-4-444-44-444-4-40000000000-4400004-40000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-2-4-4442-22-2-22200000000002-223−2323−23-220000000000000000000−23230000000000000000000000000000000
χ814-44-4-444-4-2-4-4442-22-2-22200000000002-2−2323−2323-22000000000000000000023−230000000000000000000000000000000
χ824-4-44-4-44440000-4-4-4-44440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ834-4-44-4-44440000-4-4-4-4444000000000000000000-444-4000000000000000000000000000000000000000000000000
χ844-4-4-444-444-44-4444-4-4-44-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-24-44-4-2-2222-22004-4-440000-2-200002200000000000-222-20000000000000000000000000000000000000
χ864-4-4-444-44-24-44-4-2-2222-2200-444-40000-2-2000022000000000002-2-220000000000000000000000000000000000000
χ874-4-4-444-44-2-44-44-2-2222-220000000000220000-2-200000000000000023−23−2323000000000000000000000000000000000
χ884-4-4-444-44-2-44-44-2-2222-220000000000220000-2-2000000000000000−232323−23000000000000000000000000000000000
χ8988-8-88-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-8-888-400004444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000

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