Finite Group Databasebeta

← Group #10826309

Character table — Group #10826309

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212222222444881212121212121212121224242424242424244444888846612122222244884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1
χ911111111111111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-1-11111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-1111-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-11-1-1-1-111-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-2222200-20000-2-20000000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-200-20000-2-2000000000000000022-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-200200002200000000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1000022-2-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-1000022-22222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-22000022-2-2-22-22i−2i0000−i2−i2i2i22i2i−2i−2i000022-2-2000002−20000000000−i2−i2i2i222−2−2002i−2i−i2−i2i2i20000000000002−20
χ30222-2-22-2-22000022-2-2-22-22i−2i0000−i2−i2i2i22i2i−2i−2i0000-2-222000002−20000000000−i2−i2i2i222−2−200−2i2ii2i2−i2−i2000000000000−220
χ31222-2-22-2-22000022-2-2-22-22i−2i0000i2i2−i2−i22i2i−2i−2i000022-2-200000−220000000000i2i2−i2−i2−2−222002i−2ii2i2−i2−i2000000000000−220
χ32222-2-22-2-22000022-2-2-22-22i−2i0000i2i2−i2−i22i2i−2i−2i0000-2-22200000−220000000000i2i2−i2−i2−2−22200−2i2i−i2−i2i2i20000000000002−20
χ33222-2-22-2-22000022-2-2-22-2−2i2i0000−i2−i2i2i2−2i−2i2i2i000022-2-200000−220000000000−i2−i2i2i2−2−22200−2i2i−i2−i2i2i2000000000000−220
χ34222-2-22-2-22000022-2-2-22-2−2i2i0000−i2−i2i2i2−2i−2i2i2i0000-2-22200000−220000000000−i2−i2i2i2−2−222002i−2ii2i2−i2−i20000000000002−20
χ35222-2-22-2-22000022-2-2-22-2−2i2i0000i2i2−i2−i2−2i−2i2i2i000022-2-2000002−20000000000i2i2−i2−i222−2−200−2i2ii2i2−i2−i20000000000002−20
χ36222-2-22-2-22000022-2-2-22-2−2i2i0000i2i2−i2−i2−2i−2i2i2i0000-2-222000002−20000000000i2i2−i2−i222−2−2002i−2i−i2−i2i2i2000000000000−220
χ3722-2-22-2-222-22-222-2-2-22-220022-2-200000000-2-222000000000000022-2-200000000000000002-22-2000000002-200000
χ3822-2-22-2-222-22-222-2-2-22-220022-2-200000000-2-222000000000000022-2-20000000000000000-22-2200000000-2200000
χ3922-2-22-2-222-22-222-2-2-22-2200-2-22200000000-2-2220000000000000-2-22200000000000000002-22-200000000-2200000
χ4022-2-22-2-222-22-222-2-2-22-2200-2-22200000000-2-2220000000000000-2-2220000000000000000-22-22000000002-200000
χ412-22-2-2-2222-2-222-222-2-2-22002-22-22-22-200002-22-200002-200000002-22-200002-22-200000000000002-2000000000000
χ422-22-2-2-2222-2-222-222-2-2-22002-22-2-22-2200002-22-20000-2200000002-22-20000-22-220000000000000-22000000000000
χ432-22-2-2-2222-2-222-222-2-2-2200-22-222-22-200002-22-20000-220000000-22-2200002-22-20000000000000-22000000000000
χ442-22-2-2-2222-2-222-222-2-2-2200-22-22-22-2200002-22-200002-20000000-22-220000-22-2200000000000002-2000000000000
χ452-22-2-2-222-1-2-2221-1-1111-1002-22-22-22-23−33−3-11-1100002-2000003−3-11-1133−3−3-11-113−33−3000000000-113−30000000000
χ462-22-2-2-222-1-2-2221-1-1111-1002-22-22-22-2−33−33-11-1100002-200000−33-11-11−3−333-11-11−33−33000000000-11−330000000000
χ472-22-2-2-222-1-2-2221-1-1111-1002-22-2-22-223−33−3-11-110000-22000003−3-11-1133−3−31-11-1−33−330000000001-1−330000000000
χ482-22-2-2-222-1-2-2221-1-1111-1002-22-2-22-22−33−33-11-110000-2200000−33-11-11−3−3331-11-13−33−30000000001-13−30000000000
χ492-22-2-2-222-1-2-2221-1-1111-100-22-222-22-23−33−3-11-110000-22000003−31-11-1−3−333-11-113−33−30000000001-1−330000000000
χ502-22-2-2-222-1-2-2221-1-1111-100-22-222-22-2−33−33-11-110000-2200000−331-11-133−3−3-11-11−33−330000000001-13−30000000000
χ512-22-2-2-222-1-2-2221-1-1111-100-22-22-22-223−33−3-11-1100002-2000003−31-11-1−3−3331-11-1−33−33000000000-113−30000000000
χ522-22-2-2-222-1-2-2221-1-1111-100-22-22-22-22−33−33-11-1100002-200000−331-11-133−3−31-11-13−33−3000000000-11−330000000000
χ532-2-22-22-2222-2-22-2-2-22-222002-2-2200000000-222-22-22-20000000002-2-220000000000002-200000000000000002-2000
χ542-2-22-22-2222-2-22-2-2-22-222002-2-2200000000-222-2-22-220000000002-2-22000000000000-220000000000000000-22000
χ552-2-22-22-2222-2-22-2-2-22-22200-222-200000000-222-22-22-2000000000-222-20000000000002-20000000000000000-22000
χ562-2-22-22-2222-2-22-2-2-22-22200-222-200000000-222-2-22-22000000000-222-2000000000000-2200000000000000002-2000
χ572-2-22-22-222-222-2-2-2-22-222000000000000002-2-222-22-20002-2000000002-22-200000000-220000000000002-20000000
χ582-2-22-22-222-222-2-2-2-22-222000000000000002-2-222-22-2000-2200000000-22-2200000000-22000000000000-220000000
χ592-2-22-22-222-222-2-2-2-22-222000000000000002-2-22-22-220002-2000000002-22-2000000002-2000000000000-220000000
χ602-2-22-22-222-222-2-2-2-22-222000000000000002-2-22-22-22000-2200000000-22-22000000002-20000000000002-20000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-22222000000-4000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200000040000-2-2000000000000000000000000000000000000000
χ63444-4-44-4-4-20000-2-2222-224i−4i0000−2i2−2i22i22i2−2i−2i2i2i000000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ64444-4-44-4-4-20000-2-2222-224i−4i00002i22i2−2i2−2i2−2i−2i2i2i0000000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ65444-4-44-4-4-20000-2-2222-22−4i4i0000−2i2−2i22i22i22i2i−2i−2i0000000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ66444-4-44-4-4-20000-2-2222-22−4i4i00002i22i2−2i2−2i22i2i−2i−2i000000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ6744-44-4-44-4400004-444-4-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ6844-44-4-44-4400004-444-4-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ6944-4-44-4-4444-44-44-4-4-44-440000000000000044-4-40000000000000000000000000000000000000000000000000000
χ7044-4-44-4-44-24-44-4-2222-22-200000000000000-2-2220000000000000000023−23−23230000000000000000000000000000000
χ7144-4-44-4-44-24-44-4-2222-22-200000000000000-2-22200000000000000000−232323−230000000000000000000000000000000
χ7244-4-44-4-44-2-44-44-2222-22-20044-4-40000000022-2-20000000000000-2-22200000000000000000000000000000000000
χ7344-4-44-4-44-2-44-44-2222-22-200-4-4440000000022-2-2000000000000022-2-200000000000000000000000000000000000
χ744-4444-4-4-440000-44-444-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ754-4444-4-4-440000-44-444-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ764-4444-4-4-4-200002-22-2-222000000−2i22i22i2−2i2−2i32i32i3−2i30000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ774-4444-4-4-4-200002-22-2-222000000−2i22i22i2−2i22i3−2i3−2i32i30000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ784-4444-4-4-4-200002-22-2-2220000002i2−2i2−2i22i2−2i32i32i3−2i30000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ794-4444-4-4-4-200002-22-2-2220000002i2−2i2−2i22i22i3−2i3−2i32i30000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ804-44-4-4-444444-4-4-444-4-4-4400000000000000-44-440000000000000000000000000000000000000000000000000000
χ814-44-4-4-444-244-4-42-2-2222-2000000000023−2323−232-22-200000000000−2323000000000000000000000000000000000000000
χ824-44-4-4-444-244-4-42-2-2222-20000000000−2323−23232-22-20000000000023−23000000000000000000000000000000000000000
χ834-4-44-44-44-24-4-44222-22-2-2004-4-44000000002-2-220000000000000-222-200000000000000000000000000000000000
χ844-4-44-44-44-24-4-44222-22-2-200-444-4000000002-2-2200000000000002-2-2200000000000000000000000000000000000
χ854-4-44-44-44-2-444-4222-22-2-200000000000000-222-200000004-400000000-22-220000000000000000000000000000000
χ864-4-44-44-44-2-444-4222-22-2-200000000000000-222-20000000-44000000002-22-20000000000000000000000000000000
χ874-4-4-4444-440000-4-44-444-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-4444-440000-4-44-444-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ8988-88-8-88-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8888-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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