Finite Group Databasebeta

← Group #10855267

Character table — Group #10855267

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444422444881212121212121212121224242424242424244444888846612124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ911111111111111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-111-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-2222200-20000-2-20000000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-200-20000-2-2000000000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20020000220000000000000000222200000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
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
χ2922-22-22-2-22-22-222-2-2-222-20022-2-200000000-2-222000000000000022-2-200000000000000002i2i−2i−2i00000000002i−2i000
χ3022-22-22-2-22-22-222-2-2-222-20022-2-200000000-2-222000000000000022-2-20000000000000000−2i−2i2i2i0000000000−2i2i000
χ3122-22-22-2-22-22-222-2-2-222-200-2-22200000000-2-2220000000000000-2-22200000000000000002i2i−2i−2i0000000000−2i2i000
χ3222-22-22-2-22-22-222-2-2-222-200-2-22200000000-2-2220000000000000-2-2220000000000000000−2i−2i2i2i00000000002i−2i000
χ3322-2-22-2-222000022-2-2-2-222i−2i0000−i2−i2i2i22i2i−2i−2i000022-2-2000002−20000000000−i2−i2i2i222−2−2002i−2i−i2i2−i2i20000000000002−20
χ3422-2-22-2-222000022-2-2-2-222i−2i0000−i2−i2i2i22i2i−2i−2i0000-2-222000002−20000000000−i2−i2i2i222−2−200−2i2ii2−i2i2−i2000000000000−220
χ3522-2-22-2-222000022-2-2-2-222i−2i0000i2i2−i2−i22i2i−2i−2i000022-2-200000−220000000000i2i2−i2−i2−2−222002i−2ii2−i2i2−i2000000000000−220
χ3622-2-22-2-222000022-2-2-2-222i−2i0000i2i2−i2−i22i2i−2i−2i0000-2-22200000−220000000000i2i2−i2−i2−2−22200−2i2i−i2i2−i2i20000000000002−20
χ3722-2-22-2-222000022-2-2-2-22−2i2i0000−i2−i2i2i2−2i−2i2i2i000022-2-200000−220000000000−i2−i2i2i2−2−22200−2i2i−i2i2−i2i2000000000000−220
χ3822-2-22-2-222000022-2-2-2-22−2i2i0000−i2−i2i2i2−2i−2i2i2i0000-2-22200000−220000000000−i2−i2i2i2−2−222002i−2ii2−i2i2−i20000000000002−20
χ3922-2-22-2-222000022-2-2-2-22−2i2i0000i2i2−i2−i2−2i−2i2i2i000022-2-2000002−20000000000i2i2−i2−i222−2−200−2i2ii2−i2i2−i20000000000002−20
χ4022-2-22-2-222000022-2-2-2-22−2i2i0000i2i2−i2−i2−2i−2i2i2i0000-2-222000002−20000000000i2i2−i2−i222−2−2002i−2i−i2i2−i2i2000000000000−220
χ412-22-222-2-222-2-22-2-2-22-222002-22-2000000002-22-22i−2i2i−2i0000000002-22-20000000000002i−2i000000000002i−2i00000000
χ422-22-222-2-222-2-22-2-2-22-222002-22-2000000002-22-2−2i2i−2i2i0000000002-22-2000000000000−2i2i00000000000−2i2i00000000
χ432-22-222-2-222-2-22-2-2-22-22200-22-22000000002-22-22i−2i2i−2i000000000-22-220000000000002i−2i00000000000−2i2i00000000
χ442-22-222-2-222-2-22-2-2-22-22200-22-22000000002-22-2−2i2i−2i2i000000000-22-22000000000000−2i2i000000000002i−2i00000000
χ452-22-222-2-22-222-2-2-2-22-22200000000000000-22-222i−2i2i−2i0002-20000000022-2-200000000−2i2i000000000000002i−2i00000
χ462-22-222-2-22-222-2-2-2-22-22200000000000000-22-222i−2i2i−2i000-2200000000-2-22200000000−2i2i00000000000000−2i2i00000
χ472-22-222-2-22-222-2-2-2-22-22200000000000000-22-22−2i2i−2i2i0002-20000000022-2-2000000002i−2i00000000000000−2i2i00000
χ482-22-222-2-22-222-2-2-2-22-22200000000000000-22-22−2i2i−2i2i000-2200000000-2-222000000002i−2i000000000000002i−2i00000
χ492-2-2-2-22222-2-222-222-2-22-2002-2-222-22-20000-222-200002-200000002-2-2200002-22-200000000000002-2000000000000
χ502-2-2-2-22222-2-222-222-2-22-2002-2-22-22-220000-222-20000-2200000002-2-220000-22-220000000000000-22000000000000
χ512-2-2-2-22222-2-222-222-2-22-200-222-22-22-20000-222-20000-220000000-222-200002-22-20000000000000-22000000000000
χ522-2-2-2-22222-2-222-222-2-22-200-222-2-22-220000-222-200002-20000000-222-20000-22-2200000000000002-2000000000000
χ532-2-2-2-2222-1-2-2221-1-111-11002-2-222-22-23−33−31-1-1100002-2000003−3-111-13−33−3-11-113−33−3000000000-113−30000000000
χ542-2-2-2-2222-1-2-2221-1-111-11002-2-222-22-2−33−331-1-1100002-200000−33-111-1−33−33-11-11−33−33000000000-11−330000000000
χ552-2-2-2-2222-1-2-2221-1-111-11002-2-22-22-223−33−31-1-110000-22000003−3-111-13−33−31-11-1−33−330000000001-1−330000000000
χ562-2-2-2-2222-1-2-2221-1-111-11002-2-22-22-22−33−331-1-110000-2200000−33-111-1−33−331-11-13−33−30000000001-13−30000000000
χ572-2-2-2-2222-1-2-2221-1-111-1100-222-22-22-23−33−31-1-110000-22000003−31-1-11−33−33-11-113−33−30000000001-1−330000000000
χ582-2-2-2-2222-1-2-2221-1-111-1100-222-22-22-2−33−331-1-110000-2200000−331-1-113−33−3-11-11−33−330000000001-13−30000000000
χ592-2-2-2-2222-1-2-2221-1-111-1100-222-2-22-223−33−31-1-1100002-2000003−31-1-11−33−331-11-1−33−33000000000-113−30000000000
χ602-2-2-2-2222-1-2-2221-1-111-1100-222-2-22-22−33−331-1-1100002-200000−331-1-113−33−31-11-13−33−3000000000-11−330000000000
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
χ63444-4-4-44-4400004-444-4-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ64444-4-4-44-4400004-444-4-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6544-44-44-4-444-44-44-4-4-444-40000000000000044-4-40000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-24-44-4-2222-2-2200000000000000-2-2220000000000000000023−23−23230000000000000000000000000000000
χ6744-44-44-4-4-24-44-4-2222-2-2200000000000000-2-22200000000000000000−232323−230000000000000000000000000000000
χ6844-44-44-4-4-2-44-44-2222-2-220044-4-40000000022-2-20000000000000-2-22200000000000000000000000000000000000
χ6944-44-44-4-4-2-44-44-2222-2-2200-4-4440000000022-2-2000000000000022-2-200000000000000000000000000000000000
χ7044-4-44-4-44-20000-2-22222-24i−4i0000−2i2−2i22i22i2−2i−2i2i2i000000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ7144-4-44-4-44-20000-2-22222-24i−4i00002i22i2−2i2−2i2−2i−2i2i2i0000000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ7244-4-44-4-44-20000-2-22222-2−4i4i0000−2i2−2i22i22i22i2i−2i−2i0000000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ7344-4-44-4-44-20000-2-22222-2−4i4i00002i22i2−2i2−2i22i2i−2i−2i000000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ744-444-4-4-4440000-44-444-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ754-444-4-4-4440000-44-444-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ764-444-4-4-44-200002-22-2-222000000−2i22i22i2−2i2−2i32i32i3−2i30000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ774-444-4-4-44-200002-22-2-222000000−2i22i22i2−2i22i3−2i3−2i32i30000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ784-444-4-4-44-200002-22-2-2220000002i2−2i2−2i22i2−2i32i32i3−2i30000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ794-444-4-4-44-200002-22-2-2220000002i2−2i2−2i22i22i3−2i3−2i32i30000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ804-44-444-4-4-24-4-44222-22-2-2004-44-400000000-22-220000000000000-22-2200000000000000000000000000000000000
χ814-44-444-4-4-24-4-44222-22-2-200-44-4400000000-22-2200000000000002-22-200000000000000000000000000000000000
χ824-44-444-4-4-2-444-4222-22-2-2000000000000002-22-200000004-400000000-2-2220000000000000000000000000000000
χ834-44-444-4-4-2-444-4222-22-2-2000000000000002-22-20000000-440000000022-2-20000000000000000000000000000000
χ844-4-444-44-440000-4-44-44-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ854-4-444-44-440000-4-44-44-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ864-4-4-4-4444444-4-4-444-4-44-4000000000000004-4-440000000000000000000000000000000000000000000000000000
χ874-4-4-4-4444-244-4-42-2-222-22000000000023−2323−23-222-200000000000−2323000000000000000000000000000000000000000
χ884-4-4-4-4444-244-4-42-2-222-220000000000−2323−2323-222-20000000000023−23000000000000000000000000000000000000000
χ89888-8-8-88-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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