Finite Group Databasebeta

← Group #10829218

Character table — Group #10829218

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444424444668812121212121212122424242424242424224488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-111-1-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111111-1-11-1-11111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-11
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
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-20000-2-200000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-20000-2-2000000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000022000000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-220000220000000000000000002222000000000-2000000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2-1-12211111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-1-1-2-21111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-22211-2-2-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-21122-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-211-2-21111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222211221111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-2-2-22-22-2-22222-2-2-2-22002i2i−2i−2i00002-200002-200000000000002i2i−2i−2i000000000000000022-2-200000000002i−2i000
χ30222-2-2-22-22-2-22222-2-2-2-22002i2i−2i−2i00002-200002-200000000000002i2i−2i−2i0000000000000000-2-2220000000000−2i2i000
χ31222-2-2-22-22-2-22222-2-2-2-2200−2i−2i2i2i00002-200002-20000000000000−2i−2i2i2i000000000000000022-2-20000000000−2i2i000
χ32222-2-2-22-22-2-22222-2-2-2-2200−2i−2i2i2i00002-200002-20000000000000−2i−2i2i2i0000000000000000-2-22200000000002i−2i000
χ3322-22-2-2-22200002-2-222-2-22i−2i0000−i2−i2i2i2002i2i−2i−2i002i2i−2i−2i00000002−200000000−i2−i2i2i222−2−22-2002−22−2000000000000−i2i20
χ3422-22-2-2-22200002-2-222-2-22i−2i0000−i2−i2i2i2002i2i−2i−2i00−2i−2i2i2i00000002−200000000−i2−i2i2i222−2−2-2200−22−22000000000000i2−i20
χ3522-22-2-2-22200002-2-222-2-22i−2i0000i2i2−i2−i2002i2i−2i−2i002i2i−2i−2i0000000−2200000000i2i2−i2−i2−2−2222-200−22−22000000000000i2−i20
χ3622-22-2-2-22200002-2-222-2-22i−2i0000i2i2−i2−i2002i2i−2i−2i00−2i−2i2i2i0000000−2200000000i2i2−i2−i2−2−222-22002−22−2000000000000−i2i20
χ3722-22-2-2-22200002-2-222-2-2−2i2i0000−i2−i2i2i200−2i−2i2i2i002i2i−2i−2i0000000−2200000000−i2−i2i2i2−2−222-22002−22−2000000000000i2−i20
χ3822-22-2-2-22200002-2-222-2-2−2i2i0000−i2−i2i2i200−2i−2i2i2i00−2i−2i2i2i0000000−2200000000−i2−i2i2i2−2−2222-200−22−22000000000000−i2i20
χ3922-22-2-2-22200002-2-222-2-2−2i2i0000i2i2−i2−i200−2i−2i2i2i002i2i−2i−2i00000002−200000000i2i2−i2−i222−2−2-2200−22−22000000000000−i2i20
χ4022-22-2-2-22200002-2-222-2-2−2i2i0000i2i2−i2−i200−2i−2i2i2i00−2i−2i2i2i00000002−200000000i2i2−i2−i222−2−22-2002−22−2000000000000i2−i20
χ412-2-22-222-222-22-2-2-222-2-22002i−2i2i−2i2i−2i2i−2i220000-2-200000002-200002i−2i2i−2i00002i−2i2i−2i0000000000000002-20000000000
χ422-2-22-222-222-22-2-2-222-2-22002i−2i2i−2i−2i2i−2i2i220000-2-20000000-2200002i−2i2i−2i0000−2i2i−2i2i000000000000000-220000000000
χ432-2-22-222-222-22-2-2-222-2-2200−2i2i−2i2i2i−2i2i−2i220000-2-20000000-220000−2i2i−2i2i00002i−2i2i−2i000000000000000-220000000000
χ442-2-22-222-222-22-2-2-222-2-2200−2i2i−2i2i−2i2i−2i2i220000-2-200000002-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000002-20000000000
χ452-2-22-222-2-12-22-211-1-111-1002i−2i2i−2i2i−2i2i−2i-1-1−i3i3−i3i31100000002-2−i3i300−ii−ii33−3−3−ii−ii3−33−3000000000−i3i3-110000000000
χ462-2-22-222-2-12-22-211-1-111-1002i−2i2i−2i2i−2i2i−2i-1-1i3−i3i3−i31100000002-2i3−i300−ii−ii−3−333−ii−ii−33−33000000000i3−i3-110000000000
χ472-2-22-222-2-12-22-211-1-111-1002i−2i2i−2i−2i2i−2i2i-1-1−i3i3−i3i3110000000-22−i3i300−ii−ii33−3−3i−ii−i−33−33000000000i3−i31-10000000000
χ482-2-22-222-2-12-22-211-1-111-1002i−2i2i−2i−2i2i−2i2i-1-1i3−i3i3−i3110000000-22i3−i300−ii−ii−3−333i−ii−i3−33−3000000000−i3i31-10000000000
χ492-2-22-222-2-12-22-211-1-111-100−2i2i−2i2i2i−2i2i−2i-1-1−i3i3−i3i3110000000-22−i3i300i−ii−i−3−333−ii−ii3−33−3000000000i3−i31-10000000000
χ502-2-22-222-2-12-22-211-1-111-100−2i2i−2i2i2i−2i2i−2i-1-1i3−i3i3−i3110000000-22i3−i300i−ii−i33−3−3−ii−ii−33−33000000000−i3i31-10000000000
χ512-2-22-222-2-12-22-211-1-111-100−2i2i−2i2i−2i2i−2i2i-1-1−i3i3−i3i31100000002-2−i3i300i−ii−i−3−333i−ii−i−33−33000000000−i3i3-110000000000
χ522-2-22-222-2-12-22-211-1-111-100−2i2i−2i2i−2i2i−2i2i-1-1i3−i3i3−i31100000002-2i3−i300i−ii−i33−3−3i−ii−i3−33−3000000000i3−i3-110000000000
χ532-2-2-22-22222-2-22-2-2-2-22220000000000-2200002-22-22-202-200000000002-22-200000000002-20000000000002-200000
χ542-2-2-22-22222-2-22-2-2-2-22220000000000-2200002-22-22-20-220000000000-22-2200000000002-2000000000000-2200000
χ552-2-2-22-22222-2-22-2-2-2-22220000000000-2200002-2-22-2202-200000000002-22-20000000000-22000000000000-2200000
χ562-2-2-22-22222-2-22-2-2-2-22220000000000-2200002-2-22-220-220000000000-22-220000000000-220000000000002-200000
χ572-2-2-22-2222-222-2-2-2-2-2222002-2-2200002-20000-222-22-20000000002-2-2200000000000000-2200000000002-20000000
χ582-2-2-22-2222-222-2-2-2-2-2222002-2-2200002-20000-22-22-220000000002-2-22000000000000002-20000000000-220000000
χ592-2-2-22-2222-222-2-2-2-2-222200-222-200002-20000-222-22-2000000000-222-200000000000000-220000000000-220000000
χ602-2-2-22-2222-222-2-2-2-2-222200-222-200002-20000-22-22-22000000000-222-2000000000000002-200000000002-20000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400002200000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000-2-200000000000000000000000000000000000000000
χ63444-4-4-44-4444-4-444-4-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-244-4-4-2-22222-200000000002-200002-20000000000000000023−23−23230000000000000000000000000000000
χ65444-4-4-44-4-244-4-4-2-22222-200000000002-200002-200000000000000000−232323−230000000000000000000000000000000
χ66444-4-4-44-4-2-4-444-2-22222-2004i4i−4i−4i0000-220000-220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ67444-4-4-44-4-2-4-444-2-22222-200−4i−4i4i4i0000-220000-2200000000000002i2i−2i−2i00000000000000000000000000000000000
χ6844-44-4-4-44-20000-222-2-2224i−4i0000−2i2−2i22i22i200−2i−2i2i2i000000000000022−2200000000i2i2−i2−i2−2−22200000000000000000000000
χ6944-44-4-4-44-20000-222-2-2224i−4i00002i22i2−2i2−2i200−2i−2i2i2i0000000000000−222200000000−i2−i2i2i222−2−200000000000000000000000
χ7044-44-4-4-44-20000-222-2-222−4i4i0000−2i2−2i22i22i2002i2i−2i−2i0000000000000−222200000000i2i2−i2−i222−2−200000000000000000000000
χ7144-44-4-4-44-20000-222-2-222−4i4i00002i22i2−2i2−2i2002i2i−2i−2i000000000000022−2200000000−i2−i2i2i2−2−22200000000000000000000000
χ7244-4-444-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7344-4-444-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ744-4444-4-4-440000-44-44-44-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ754-4444-4-4-440000-44-44-44-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ764-4444-4-4-4-200002-22-22-2200000022−22−22220023−23−232300000000000000000000000−222−26−6−6600000000000000000000000
χ774-4444-4-4-4-200002-22-22-2200000022−22−222200−232323−2300000000000000000000000−222−2−666−600000000000000000000000
χ784-4444-4-4-4-200002-22-22-22000000−222222−220023−23−2323000000000000000000000002−2−22−666−600000000000000000000000
χ794-4444-4-4-4-200002-22-22-22000000−222222−2200−232323−23000000000000000000000002−2−226−6−6600000000000000000000000
χ804-44-4-44-4440000-444-44-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ814-44-4-44-4440000-444-44-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ824-4-44-444-44-44-44-4-444-4-440000000000-4-40000440000000000000000000000000000000000000000000000000000
χ834-4-44-444-4-2-44-4422-2-222-2000000000022−2i32i3−2i32i3-2-20000000002i3−2i300000000000000000000000000000000000000000
χ844-4-44-444-4-2-44-4422-2-222-20000000000222i3−2i32i3−2i3-2-2000000000−2i32i300000000000000000000000000000000000000000
χ854-4-4-44-444-24-4-442222-2-2-200000000002-20000-22000004-40000000000-22-220000000000000000000000000000000
χ864-4-4-44-444-24-4-442222-2-2-200000000002-20000-2200000-4400000000002-22-20000000000000000000000000000000
χ874-4-4-44-444-2-444-42222-2-2-2004-4-440000-2200002-20000000000000-222-200000000000000000000000000000000000
χ884-4-4-44-444-2-444-42222-2-2-200-444-40000-2200002-200000000000002-2-2200000000000000000000000000000000000
χ8988-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000

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