Finite Group Databasebeta

← Group #10868036

Character table — Group #10868036

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444424444668812121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-111-111-1-1-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-11111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-111111-1-1-1
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
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-20000-2-200000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-20000-2-2000000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000022000000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-22000022000000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-2-2-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-22211-2-2-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-21122-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-2-1-12211111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-1-1-2-21111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-211-2-21111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222211221111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-2-2-22-2222-2-222-2-222-2-200000000002-200002-22i2i−2i−2i02i−2i00000000002i2i−2i−2i00000000002i−2i000000000000002-2000
χ3022-2-2-22-2222-2-222-2-222-2-200000000002-200002-22i2i−2i−2i0−2i2i0000000000−2i−2i2i2i00000000002i−2i00000000000000-22000
χ3122-2-2-22-2222-2-222-2-222-2-200000000002-200002-2−2i−2i2i2i02i−2i00000000002i2i−2i−2i0000000000−2i2i00000000000000-22000
χ3222-2-2-22-2222-2-222-2-222-2-200000000002-200002-2−2i−2i2i2i0−2i2i0000000000−2i−2i2i2i0000000000−2i2i000000000000002-2000
χ3322-2-2-22-222-222-22-2-222-2-22i2i−2i−2i000000-220000-222i2i−2i−2i0000000002i2i−2i−2i00000000000000−2i2i0000000002-200000000
χ3422-2-2-22-222-222-22-2-222-2-22i2i−2i−2i000000-220000-22−2i−2i2i2i0000000002i2i−2i−2i000000000000002i−2i000000000-2200000000
χ3522-2-2-22-222-222-22-2-222-2-2−2i−2i2i2i000000-220000-222i2i−2i−2i000000000−2i−2i2i2i00000000000000−2i2i000000000-2200000000
χ3622-2-2-22-222-222-22-2-222-2-2−2i−2i2i2i000000-220000-22−2i−2i2i2i000000000−2i−2i2i2i000000000000002i−2i0000000002-200000000
χ372-222-2-2-2220000-22-22-22-200002i−2i22−2−2002i2i−2i−2i002i−2i2i−2i0000000−i2i20000000022−2−2−i2−i2i2i22-200−i2−i2i2i20000000000002−20
χ382-222-2-2-2220000-22-22-22-200002i−2i22−2−2002i2i−2i−2i00−2i2i−2i2i0000000−i2i20000000022−2−2−i2−i2i2i2-2200i2i2−i2−i2000000000000−220
χ392-222-2-2-2220000-22-22-22-200002i−2i−2−222002i2i−2i−2i002i−2i2i−2i0000000i2−i200000000−2−222i2i2−i2−i22-200i2i2−i2−i2000000000000−220
χ402-222-2-2-2220000-22-22-22-200002i−2i−2−222002i2i−2i−2i00−2i2i−2i2i0000000i2−i200000000−2−222i2i2−i2−i2-2200−i2−i2i2i20000000000002−20
χ412-222-2-2-2220000-22-22-22-20000−2i2i22−2−200−2i−2i2i2i002i−2i2i−2i0000000i2−i20000000022−2−2i2i2−i2−i2-2200−i2−i2i2i2000000000000−220
χ422-222-2-2-2220000-22-22-22-20000−2i2i22−2−200−2i−2i2i2i00−2i2i−2i2i0000000i2−i20000000022−2−2i2i2−i2−i22-200i2i2−i2−i20000000000002−20
χ432-222-2-2-2220000-22-22-22-20000−2i2i−2−22200−2i−2i2i2i002i−2i2i−2i0000000−i2i200000000−2−222−i2−i2i2i2-2200i2i2−i2−i20000000000002−20
χ442-222-2-2-2220000-22-22-22-20000−2i2i−2−22200−2i−2i2i2i00−2i2i−2i2i0000000−i2i200000000−2−222−i2−i2i2i22-200−i2−i2i2i2000000000000−220
χ452-22-2-222-22-22-22-222-22-2-22i−2i2i−2i002-22-2-2-200002200000002i−2i00002i−2i2i−2i00002-22-200000000000002i−2i000000000000
χ462-22-2-222-22-22-22-222-22-2-22i−2i2i−2i00-22-22-2-20000220000000−2i2i00002i−2i2i−2i0000-22-220000000000000−2i2i000000000000
χ472-22-2-222-22-22-22-222-22-2-2−2i2i−2i2i002-22-2-2-20000220000000−2i2i0000−2i2i−2i2i00002-22-20000000000000−2i2i000000000000
χ482-22-2-222-22-22-22-222-22-2-2−2i2i−2i2i00-22-22-2-200002200000002i−2i0000−2i2i−2i2i0000-22-2200000000000002i−2i000000000000
χ492-22-2-222-2-1-22-221-1-11-1112i−2i2i−2i002-22-211−i3i3−i3i3-1-100000002i−2i−i3i300−ii−ii3−33−3-11-11−i3i3−i3i3000000000−ii3−30000000000
χ502-22-2-222-2-1-22-221-1-11-1112i−2i2i−2i002-22-211i3−i3i3−i3-1-100000002i−2ii3−i300−ii−ii−33−33-11-11i3−i3i3−i3000000000−ii−330000000000
χ512-22-2-222-2-1-22-221-1-11-1112i−2i2i−2i00-22-2211−i3i3−i3i3-1-10000000−2i2i−i3i300−ii−ii3−33−31-11-1i3−i3i3−i3000000000i−i−330000000000
χ522-22-2-222-2-1-22-221-1-11-1112i−2i2i−2i00-22-2211i3−i3i3−i3-1-10000000−2i2ii3−i300−ii−ii−33−331-11-1−i3i3−i3i3000000000i−i3−30000000000
χ532-22-2-222-2-1-22-221-1-11-111−2i2i−2i2i002-22-211−i3i3−i3i3-1-10000000−2i2i−i3i300i−ii−i−33−33-11-11−i3i3−i3i3000000000i−i−330000000000
χ542-22-2-222-2-1-22-221-1-11-111−2i2i−2i2i002-22-211i3−i3i3−i3-1-10000000−2i2ii3−i300i−ii−i3−33−3-11-11i3−i3i3−i3000000000i−i3−30000000000
χ552-22-2-222-2-1-22-221-1-11-111−2i2i−2i2i00-22-2211−i3i3−i3i3-1-100000002i−2i−i3i300i−ii−i−33−331-11-1i3−i3i3−i3000000000−ii3−30000000000
χ562-22-2-222-2-1-22-221-1-11-111−2i2i−2i2i00-22-2211i3−i3i3−i3-1-100000002i−2ii3−i300i−ii−i3−33−31-11-1−i3i3−i3i3000000000−ii−330000000000
χ572-2-2222-2-2222-2-2-2-2-2-22222-2-220000002-20000-2200000000000002-2-2200000000000000002i−2i2i−2i000000002i−2i00000
χ582-2-2222-2-2222-2-2-2-2-2-22222-2-220000002-20000-2200000000000002-2-220000000000000000−2i2i−2i2i00000000−2i2i00000
χ592-2-2222-2-2222-2-2-2-2-2-2222-222-20000002-20000-220000000000000-222-200000000000000002i−2i2i−2i00000000−2i2i00000
χ602-2-2222-2-2222-2-2-2-2-2-2222-222-20000002-20000-220000000000000-222-20000000000000000−2i2i−2i2i000000002i−2i00000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400002200000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000040000-2-200000000000000000000000000000000000000000
χ63444-44-4-4-44000044-4-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ64444-44-4-4-44000044-4-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ65444-44-4-4-4-20000-2-22222-200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ66444-44-4-4-4-20000-2-22222-200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ67444-44-4-4-4-20000-2-22222-2000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ68444-44-4-4-4-20000-2-22222-2000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ6944-44-4-44-4400004-44-4-44-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7044-44-4-44-4400004-44-4-44-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ7144-4-4-44-44-24-4-44-222-2-2220000000000-220000-22000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ7244-4-4-44-44-24-4-44-222-2-2220000000000-220000-2200000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ7344-4-4-44-44-2-444-4-222-2-2224i4i−4i−4i0000002-200002-20000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7444-4-4-44-44-2-444-4-222-2-222−4i−4i4i4i0000002-200002-200000000000002i2i−2i−2i00000000000000000000000000000000000
χ754-444-4-4-44-200002-22-22-2200004i−4i2222−22−2200−2i−2i2i2i0000000000000−2i22i200000000−2−222i2i2−i2−i200000000000000000000000
χ764-444-4-4-44-200002-22-22-2200004i−4i−22−22222200−2i−2i2i2i00000000000002i2−2i20000000022−2−2−i2−i2i2i200000000000000000000000
χ774-444-4-4-44-200002-22-22-220000−4i4i2222−22−22002i2i−2i−2i00000000000002i2−2i200000000−2−222−i2−i2i2i200000000000000000000000
χ784-444-4-4-44-200002-22-22-220000−4i4i−22−222222002i2i−2i−2i0000000000000−2i22i20000000022−2−2i2i2−i2−i200000000000000000000000
χ794-44-4-444-444-44-4-444-44-4-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-24-44-42-2-22-2220000000000-2-2−2i32i3−2i32i3220000000002i3−2i300000000000000000000000000000000000000000
χ814-44-4-444-4-24-44-42-2-22-2220000000000-2-22i3−2i32i3−2i322000000000−2i32i300000000000000000000000000000000000000000
χ824-4-4444-4-44-4-444-4-4-4-44440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-244-4-42222-2-2-24-4-44000000-2200002-20000000000000-222-200000000000000000000000000000000000
χ844-4-4444-4-4-244-4-42222-2-2-2-444-4000000-2200002-200000000000002-2-2200000000000000000000000000000000000
χ854-4-4444-4-4-2-4-4442222-2-2-200000000002-20000-2200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ864-4-4444-4-4-2-4-4442222-2-2-200000000002-20000-22000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ874-4-4-44-44440000-4-444-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-44-44440000-4-444-4-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ8988-88-8-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-4000044-4-444-40000000000000000000000000000000000000000000000000000000000000000000000

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