Finite Group Databasebeta

← Group #10852257

Character table — Group #10852257

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424224488884121212122244444884
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
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-111-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-2000000-2-20000000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-2000000-2-2000000000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-2222-2-222-2-22-2-20022-2-20000220000-2-222-2-200000000022-2-20000000000002-2000000000002-200000000
χ30222-2-22-2-2222-2-222-2-22-2-20022-2-20000220000-2-2-2-22200000000022-2-2000000000000-2200000000000-2200000000
χ31222-2-22-2-2222-2-222-2-22-2-200-2-2220000220000-2-222-2-2000000000-2-2220000000000002-200000000000-2200000000
χ32222-2-22-2-2222-2-222-2-22-2-200-2-2220000220000-2-2-2-222000000000-2-222000000000000-22000000000002-200000000
χ33222-2-22-2-22-2-22222-2-22-2-20000000000-2-200002222-2-202i−2i00000000002i2i−2i−2i00000000-22000000000000002i−2i00000
χ34222-2-22-2-22-2-22222-2-22-2-20000000000-2-200002222-2-20−2i2i0000000000−2i−2i2i2i00000000-2200000000000000−2i2i00000
χ35222-2-22-2-22-2-22222-2-22-2-20000000000-2-2000022-2-22202i−2i00000000002i2i−2i−2i000000002-200000000000000−2i2i00000
χ36222-2-22-2-22-2-22222-2-22-2-20000000000-2-2000022-2-2220−2i2i0000000000−2i−2i2i2i000000002-2000000000000002i−2i00000
χ3722-22-2-22-2200002-2-22-22-22i−2i0000−i2−i2i2i2002i2i−2i−2i002i−2i2i−2i000002−20000000000−i2−i2i2i222−2−2002-222−2−2000000000000−i2i20
χ3822-22-2-22-2200002-2-22-22-22i−2i0000−i2−i2i2i2002i2i−2i−2i00−2i2i−2i2i000002−20000000000−i2−i2i2i222−2−200-22−2−222000000000000i2−i20
χ3922-22-2-22-2200002-2-22-22-22i−2i0000i2i2−i2−i2002i2i−2i−2i002i−2i2i−2i00000−220000000000i2i2−i2−i2−2−222002-2−2−222000000000000i2−i20
χ4022-22-2-22-2200002-2-22-22-22i−2i0000i2i2−i2−i2002i2i−2i−2i00−2i2i−2i2i00000−220000000000i2i2−i2−i2−2−22200-2222−2−2000000000000−i2i20
χ4122-22-2-22-2200002-2-22-22-2−2i2i0000−i2−i2i2i200−2i−2i2i2i002i−2i2i−2i00000−220000000000−i2−i2i2i2−2−22200-2222−2−2000000000000i2−i20
χ4222-22-2-22-2200002-2-22-22-2−2i2i0000−i2−i2i2i200−2i−2i2i2i00−2i2i−2i2i00000−220000000000−i2−i2i2i2−2−222002-2−2−222000000000000−i2i20
χ4322-22-2-22-2200002-2-22-22-2−2i2i0000i2i2−i2−i200−2i−2i2i2i002i−2i2i−2i000002−20000000000i2i2−i2−i222−2−200-22−2−222000000000000−i2i20
χ4422-22-2-22-2200002-2-22-22-2−2i2i0000i2i2−i2−i200−2i−2i2i2i00−2i2i−2i2i000002−20000000000i2i2−i2−i222−2−2002-222−2−2000000000000i2−i20
χ452-2-2222-2-222-22-2-2-2-2-2222002-22-200002-200002-200000000000002-22-200000000000000002i−2i2i−2i00000000002i−2i000
χ462-2-2222-2-222-22-2-2-2-2-2222002-22-200002-200002-200000000000002-22-20000000000000000−2i2i−2i2i0000000000−2i2i000
χ472-2-2222-2-222-22-2-2-2-2-222200-22-2200002-200002-20000000000000-22-2200000000000000002i−2i2i−2i0000000000−2i2i000
χ482-2-2222-2-222-22-2-2-2-2-222200-22-2200002-200002-20000000000000-22-220000000000000000−2i2i−2i2i00000000002i−2i000
χ492-2-2-2-222222-2-22-2-2222-2-2002-2-222-22-22-20000-2200000002-200002-2-2200002-22-200000000000002-2000000000000
χ502-2-2-2-222222-2-22-2-2222-2-2002-2-22-22-222-20000-220000000-2200002-2-220000-22-220000000000000-22000000000000
χ512-2-2-2-222222-2-22-2-2222-2-200-222-22-22-22-20000-220000000-220000-222-200002-22-20000000000000-22000000000000
χ522-2-2-2-222222-2-22-2-2222-2-200-222-2-22-222-20000-2200000002-20000-222-20000-22-2200000000000002-2000000000000
χ532-2-2-2-2222-12-2-2211-1-1-111002-2-222-22-2-113−33−31-100000002-2003−3-111-13−33−3-11-113−33−3000000000-113−30000000000
χ542-2-2-2-2222-12-2-2211-1-1-111002-2-222-22-2-11−33−331-100000002-200−33-111-1−33−33-11-11−33−33000000000-11−330000000000
χ552-2-2-2-2222-12-2-2211-1-1-111002-2-22-22-22-113−33−31-10000000-22003−3-111-13−33−31-11-1−33−330000000001-1−330000000000
χ562-2-2-2-2222-12-2-2211-1-1-111002-2-22-22-22-11−33−331-10000000-2200−33-111-1−33−331-11-13−33−30000000001-13−30000000000
χ572-2-2-2-2222-12-2-2211-1-1-11100-222-22-22-2-113−33−31-10000000-22003−31-1-11−33−33-11-113−33−30000000001-1−330000000000
χ582-2-2-2-2222-12-2-2211-1-1-11100-222-22-22-2-11−33−331-10000000-2200−331-1-113−33−3-11-11−33−330000000001-13−30000000000
χ592-2-2-2-2222-12-2-2211-1-1-11100-222-2-22-22-113−33−31-100000002-2003−31-1-11−33−331-11-1−33−33000000000-113−30000000000
χ602-2-2-2-2222-12-2-2211-1-1-11100-222-2-22-22-11−33−331-100000002-200−331-1-113−33−31-11-13−33−3000000000-11−330000000000
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
χ63444-4-44-4-4-244-4-4-2-222-2220044-4-40000-2-20000220000000000000-2-22200000000000000000000000000000000000
χ64444-4-44-4-4-244-4-4-2-222-22200-4-4440000-2-2000022000000000000022-2-200000000000000000000000000000000000
χ65444-4-44-4-4-2-4-444-2-222-2220000000000220000-2-2000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ66444-4-44-4-4-2-4-444-2-222-2220000000000220000-2-200000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ6744-44-4-44-4-20000-222-22-224i−4i0000−2i2−2i22i22i200−2i−2i2i2i0000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ6844-44-4-44-4-20000-222-22-224i−4i00002i22i2−2i2−2i200−2i−2i2i2i00000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ6944-44-4-44-4-20000-222-22-22−4i4i0000−2i2−2i22i22i2002i2i−2i−2i00000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ7044-44-4-44-4-20000-222-22-22−4i4i00002i22i2−2i2−2i2002i2i−2i−2i0000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ7144-4-44-4-44400004-44-4-4-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ7244-4-44-4-44400004-44-4-4-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ734-444-4-4-4440000-444-4-44-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ744-444-4-4-4440000-444-4-44-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ754-44-44-44-440000-44-44-4-44000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ764-44-44-44-440000-44-44-4-440000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ774-44-44-44-4-200002-22-222-2000000−2i22i22i2−2i200−2i32i32i3−2i300000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ784-44-44-44-4-200002-22-222-2000000−2i22i22i2−2i2002i3−2i3−2i32i300000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ794-44-44-44-4-200002-22-222-20000002i2−2i2−2i22i200−2i32i32i3−2i300000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ804-44-44-44-4-200002-22-222-20000002i2−2i2−2i22i2002i3−2i3−2i32i300000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ814-4-4444-4-44-44-44-4-4-4-44440000000000-440000-440000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-24-44-42222-2-2-2004-44-40000-220000-220000000000000-22-2200000000000000000000000000000000000
χ834-4-4444-4-4-24-44-42222-2-2-200-44-440000-220000-2200000000000002-22-200000000000000000000000000000000000
χ844-4-4444-4-4-2-44-442222-2-2-200000000002-200002-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ854-4-4444-4-4-2-44-442222-2-2-200000000002-200002-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ864-4-4-4-44444-444-4-4-4444-4-40000000000-4400004-40000000000000000000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-422-2-2-22200000000002-223−2323−23-2200000000000−2323000000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-422-2-2-22200000000002-2−2323−2323-220000000000023−23000000000000000000000000000000000000000
χ8988-8-88-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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