Finite Group Databasebeta

← Group #10868016

Character table — Group #10868016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-111-1-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-11-1-11111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-1111-1-11111-1
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
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-2000000-2-2000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-220000002200000000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-222-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
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
χ2922-22-2-22-2200002-2-22-2-222-20000−i2−i2i2i20022-2-2002i2i−2i−2i00000−i2i20000000000−i2−i2i2i2−i2−i2i2i22i−2i0022−2−20000000000002−20
χ3022-22-2-22-2200002-2-22-2-222-20000−i2−i2i2i20022-2-200−2i−2i2i2i00000−i2i20000000000−i2−i2i2i2−i2−i2i2i2−2i2i00−2−222000000000000−220
χ3122-22-2-22-2200002-2-22-2-222-20000i2i2−i2−i20022-2-2002i2i−2i−2i00000i2−i20000000000i2i2−i2−i2i2i2−i2−i22i−2i00−2−222000000000000−220
χ3222-22-2-22-2200002-2-22-2-222-20000i2i2−i2−i20022-2-200−2i−2i2i2i00000i2−i20000000000i2i2−i2−i2i2i2−i2−i2−2i2i0022−2−20000000000002−20
χ3322-22-2-22-2200002-2-22-2-22-220000−i2−i2i2i200-2-222002i2i−2i−2i00000i2−i20000000000−i2−i2i2i2i2i2−i2−i2−2i2i0022−2−2000000000000−220
χ3422-22-2-22-2200002-2-22-2-22-220000−i2−i2i2i200-2-22200−2i−2i2i2i00000i2−i20000000000−i2−i2i2i2i2i2−i2−i22i−2i00−2−2220000000000002−20
χ3522-22-2-22-2200002-2-22-2-22-220000i2i2−i2−i200-2-222002i2i−2i−2i00000−i2i20000000000i2i2−i2−i2−i2−i2i2i2−2i2i00−2−2220000000000002−20
χ3622-22-2-22-2200002-2-22-2-22-220000i2i2−i2−i200-2-22200−2i−2i2i2i00000−i2i20000000000i2i2−i2−i2−i2−i2i2i22i−2i0022−2−2000000000000−220
χ3722-2-22-2-2222-2-2222-2-22-2-20000000000220000-2-22i−2i2i−2i0002-20000000022-2-200000000002i−2i0000000000002i−2i00000
χ3822-2-22-2-2222-2-2222-2-22-2-20000000000220000-2-22i−2i2i−2i000-2200000000-2-22200000000002i−2i000000000000−2i2i00000
χ3922-2-22-2-2222-2-2222-2-22-2-20000000000220000-2-2−2i2i−2i2i0002-20000000022-2-20000000000−2i2i000000000000−2i2i00000
χ4022-2-22-2-2222-2-2222-2-22-2-20000000000220000-2-2−2i2i−2i2i000-2200000000-2-2220000000000−2i2i0000000000002i−2i00000
χ4122-2-22-2-222-222-222-2-22-2-2002i2i−2i−2i0000-2-20000222i−2i2i−2i0000000002i2i−2i−2i00000000000000−2i2i00000000002-20000000
χ4222-2-22-2-222-222-222-2-22-2-2002i2i−2i−2i0000-2-2000022−2i2i−2i2i0000000002i2i−2i−2i000000000000002i−2i0000000000-220000000
χ4322-2-22-2-222-222-222-2-22-2-200−2i−2i2i2i0000-2-20000222i−2i2i−2i000000000−2i−2i2i2i00000000000000−2i2i0000000000-220000000
χ4422-2-22-2-222-222-222-2-22-2-200−2i−2i2i2i0000-2-2000022−2i2i−2i2i000000000−2i−2i2i2i000000000000002i−2i00000000002-20000000
χ452-2222-2-2-22-22-22-222-2-2-22002i−2i2i−2i00002-200002-200000000000002i−2i2i−2i00000000000000002-22-200000000002i−2i000
χ462-2222-2-2-22-22-22-222-2-2-22002i−2i2i−2i00002-200002-200000000000002i−2i2i−2i0000000000000000-22-220000000000−2i2i000
χ472-2222-2-2-22-22-22-222-2-2-2200−2i2i−2i2i00002-200002-20000000000000−2i2i−2i2i00000000000000002-22-20000000000−2i2i000
χ482-2222-2-2-22-22-22-222-2-2-2200−2i2i−2i2i00002-200002-20000000000000−2i2i−2i2i0000000000000000-22-2200000000002i−2i000
χ492-2-2-2222-2222-2-2-22-22-22-2002-2-222i−2i2i−2i-2200002-2000002i−2i0000002-2-2200002i−2i2i−2i0000000000000002i−2i0000000000
χ502-2-2-2222-2222-2-2-22-22-22-2002-2-22−2i2i−2i2i-2200002-200000−2i2i0000002-2-220000−2i2i−2i2i000000000000000−2i2i0000000000
χ512-2-2-2222-2222-2-2-22-22-22-200-222-22i−2i2i−2i-2200002-200000−2i2i000000-222-200002i−2i2i−2i000000000000000−2i2i0000000000
χ522-2-2-2222-2222-2-2-22-22-22-200-222-2−2i2i−2i2i-2200002-2000002i−2i000000-222-20000−2i2i−2i2i0000000000000002i−2i0000000000
χ532-2-2-2222-2-122-2-21-11-11-11002-2-222i−2i2i−2i1-13−33−3-11000002i−2i00003−3-111-13−33−3−ii−ii−i3i3−i3i3000000000−i3i3−ii0000000000
χ542-2-2-2222-2-122-2-21-11-11-11002-2-222i−2i2i−2i1-1−33−33-11000002i−2i0000−33-111-1−33−33−ii−iii3−i3i3−i3000000000i3−i3−ii0000000000
χ552-2-2-2222-2-122-2-21-11-11-11002-2-22−2i2i−2i2i1-13−33−3-1100000−2i2i00003−3-111-13−33−3i−ii−ii3−i3i3−i3000000000i3−i3i−i0000000000
χ562-2-2-2222-2-122-2-21-11-11-11002-2-22−2i2i−2i2i1-1−33−33-1100000−2i2i0000−33-111-1−33−33i−ii−i−i3i3−i3i3000000000−i3i3i−i0000000000
χ572-2-2-2222-2-122-2-21-11-11-1100-222-22i−2i2i−2i1-13−33−3-1100000−2i2i00003−31-1-11−33−33−ii−ii−i3i3−i3i3000000000i3−i3i−i0000000000
χ582-2-2-2222-2-122-2-21-11-11-1100-222-22i−2i2i−2i1-1−33−33-1100000−2i2i0000−331-1-113−33−3−ii−iii3−i3i3−i3000000000−i3i3i−i0000000000
χ592-2-2-2222-2-122-2-21-11-11-1100-222-2−2i2i−2i2i1-13−33−3-11000002i−2i00003−31-1-11−33−33i−ii−ii3−i3i3−i3000000000−i3i3−ii0000000000
χ602-2-2-2222-2-122-2-21-11-11-1100-222-2−2i2i−2i2i1-1−33−33-11000002i−2i0000−331-1-113−33−3i−ii−i−i3i3−i3i3000000000i3−i3−ii0000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-44-4-4400004-44-4-44-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-4-44-4-4400004-44-4-44-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-44-4-44-4-20000-222-222-24-40000−2i2−2i22i22i200-2-22200000000000−2i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ6644-44-4-44-4-20000-222-222-24-400002i22i2−2i2−2i200-2-222000000000002i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ6744-44-4-44-4-20000-222-222-2-440000−2i2−2i22i22i20022-2-2000000000002i2−2i20000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ6844-44-4-44-4-20000-222-222-2-4400002i22i2−2i2−2i20022-2-200000000000−2i22i20000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ6944-4-44-4-44-24-4-44-2-222-2220000000000-2-200002200000004-400000000-2-2220000000000000000000000000000000
χ7044-4-44-4-44-24-4-44-2-222-2220000000000-2-20000220000000-440000000022-2-20000000000000000000000000000000
χ7144-4-44-4-44-2-444-4-2-222-222004i4i−4i−4i0000220000-2-20000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7244-4-44-4-44-2-444-4-2-222-22200−4i−4i4i4i0000220000-2-200000000000002i2i−2i−2i00000000000000000000000000000000000
χ734-4444-4-4-444-44-4-444-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ744-4444-4-4-4-24-44-42-2-2222-200000000002-200002-20000000000000000023−23−23230000000000000000000000000000000
χ754-4444-4-4-4-24-44-42-2-2222-200000000002-200002-200000000000000000−232323−230000000000000000000000000000000
χ764-4444-4-4-4-2-44-442-2-2222-2004i−4i4i−4i0000-220000-220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ774-4444-4-4-4-2-44-442-2-2222-200−4i4i−4i4i0000-220000-2200000000000002i−2i2i−2i00000000000000000000000000000000000
χ784-44-4-4-44440000-4-4444-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ794-44-4-4-44440000-4-4444-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ804-44-4-4-444-2000022-2-2-22200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ814-44-4-4-444-2000022-2-2-22200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ824-44-4-4-444-2000022-2-2-222000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ834-44-4-4-444-2000022-2-2-222000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ844-4-44-44-4440000-4-4-4-444400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ854-4-44-44-4440000-4-4-4-4444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ864-4-4-4444-44-4-444-44-44-44-400000000004-40000-440000000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-2-4-4442-22-22-220000000000-2223−2323−232-200000000000−2323000000000000000000000000000000000000000
χ884-4-4-4444-4-2-4-4442-22-22-220000000000-22−2323−23232-20000000000023−23000000000000000000000000000000000000000
χ89888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-400004444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000

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