Finite Group Databasebeta

← Group #10694903

Character table — Group #10694903

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1222222234444446661212121224666666888888881212121212122424242424242424242424242424242488882424242424242424444488882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-1
χ10111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-11-11
χ11111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-11-11
χ12111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-1
χ13111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ14111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−i−iiiii−i−i-111-1
χ15111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ16111111-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ17222222222-2-2-2-2-2-2222-2-2-2-22-222222200000000-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-2-2-2222-2-2-2-22-222222200000000-2-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i0000
χ1922222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ2222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ23222222-2-22-2-222222222222-2-222-2-2-2-200000000-2-2-222-2000000000000000000000000000000002-2-220000
χ24222222-2-22-2-222222222222-2-222-2-2-2-200000000-2-2-222-200000000000000000000000000000000-222-20000
χ25222222-2-2-122-2-2-2-2-1-1-11111-22-1-111112222-2-2-2-2-1-1-111-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii000000000000
χ26222222-2-2-122-2-2-2-2-1-1-11111-22-1-111112222-2-2-2-2-1-1-111-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i000000000000
χ27222222-2-2-122-2-2-2-2-1-1-11111-22-1-11111-2-2-2-22222-1-1-111-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ28222222-2-2-122-2-2-2-2-1-1-11111-22-1-11111-2-2-2-22222-1-1-111-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ292222-2-222222-2-222222-2-2-2-2-2-2-2-222-2-222-2-222-2-22-2-22222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-222222-2-222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222-2-2222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-2222-2-222-2-22222222-22-2-222-2-200000000-222-2-2-200000000000000000000000000002-22-200000000
χ322222-2-2222-2-222-2-22222222-22-2-222-2-200000000-222-2-2-20000000000000000000000000000-22-2200000000
χ332222-2-222-122-2-222-1-1-11111-2-211-1-11122-2-222-2-2-111-1-1-1-1-1-1-11111-1-1-1-1111100003−33−33−33−3000000000000
χ342222-2-222-122-2-222-1-1-11111-2-211-1-11122-2-222-2-2-111-1-1-1-1-1-1-11111-1-1-1-111110000−33−33−33−33000000000000
χ352222-2-222-122-2-222-1-1-11111-2-211-1-111-2-222-2-222-111-1-1-11111-1-1-1-11111-1-1-1-100003−33−3−33−33000000000000
χ362222-2-222-122-2-222-1-1-11111-2-211-1-111-2-222-2-222-111-1-1-11111-1-1-1-11111-1-1-1-10000−33−333−33−3000000000000
χ372222-2-2-2-222222-2-222222222-2-2-2-2-22222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ382222-2-2-2-222222-2-222222222-2-2-2-2-222-2-22222-2-22-2-2-2-22-2-2-2-222222222-2-2-2-2000000000000000000000000
χ392222-2-2-2-22-2-2-2-222222-2-2-2-222-2-2-2-22200000000-22222-200000000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-22-2-2-2-222222-2-2-2-222-2-2-2-22200000000-22222-20000000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-12222-2-2-1-1-1-1-1-1-12-21111-1-122-2-2-2-222-11111-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-2-2-12222-2-2-1-1-1-1-1-1-12-21111-1-122-2-2-2-222-11111-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-2-2-12222-2-2-1-1-1-1-1-1-12-21111-1-1-2-22222-2-2-11111-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-2-2-12222-2-2-1-1-1-1-1-1-12-21111-1-1-2-22222-2-2-11111-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ4544444444-2-4-4-4-4-4-4-2-2-222224-4-2-2-2-2-2-2000000002222220000000000000000000000000000000000000000
χ46444444-4-4-2-4-44444-2-2-2-2-2-2-2-4-4-2-2222200000000222-2-220000000000000000000000000000000000000000
χ474444-4-444-2-4-444-4-4-2-2-2-2-2-2-2-4422-2-222000000002-2-22220000000000000000000000000000000000000000
χ484444-4-4-4-4-2-4-4-4-444-2-2-22222442222-2-2000000002-2-2-2-220000000000000000000000000000000000000000
χ4944-4-4004-440000004-4-4000000004-40000−2i22i200−2i22i20000000000−2i2−2i22i22i20000−2i2−2i22i22i2000000000000000000000000
χ5044-4-4004-440000004-4-4000000004-400002i2−2i2002i2−2i200000000002i22i2−2i2−2i200002i22i2−2i2−2i2000000000000000000000000
χ5144-4-4004-4-2000000-2222323−23−230000-220000−2i22i200−2i22i2023−23000i6i6−i6−i6i2i2−i2−i2i6i6−i6−i6i2i2−i2−i2000000000000000000000000
χ5244-4-4004-4-2000000-2222323−23−230000-2200002i2−2i2002i2−2i2023−23000−i6−i6i6i6−i2−i2i2i2−i6−i6i6i6−i2−i2i2i2000000000000000000000000
χ5344-4-4004-4-2000000-222−23−2323230000-220000−2i22i200−2i22i20−2323000−i6−i6i6i6i2i2−i2−i2−i6−i6i6i6i2i2−i2−i2000000000000000000000000
χ5444-4-4004-4-2000000-222−23−2323230000-2200002i2−2i2002i2−2i20−2323000i6i6−i6−i6−i2−i2i2i2i6i6−i6−i6−i2−i2i2i2000000000000000000000000
χ5544-4-400-4440000004-4-400000000-440000−2i22i2002i2−2i20000000000−2i2−2i22i22i200002i22i2−2i2−2i2000000000000000000000000
χ5644-4-400-4440000004-4-400000000-4400002i2−2i200−2i22i200000000002i22i2−2i2−2i20000−2i2−2i22i22i2000000000000000000000000
χ5744-4-400-44-2000000-2222323−23−2300002-20000−2i22i2002i2−2i20−2323000−i6−i6i6i6i2i2−i2−i2i6i6−i6−i6−i2−i2i2i2000000000000000000000000
χ5844-4-400-44-2000000-2222323−23−2300002-200002i2−2i200−2i22i20−2323000i6i6−i6−i6−i2−i2i2i2−i6−i6i6i6i2i2−i2−i2000000000000000000000000
χ5944-4-400-44-2000000-222−23−23232300002-20000−2i22i2002i2−2i2023−23000i6i6−i6−i6i2i2−i2−i2−i6−i6i6i6−i2−i2i2i2000000000000000000000000
χ6044-4-400-44-2000000-222−23−23232300002-200002i2−2i200−2i22i2023−23000−i6−i6i6i6−i2−i2i2i2i6i6−i6−i6i2i2−i2−i2000000000000000000000000
χ614-44-44-4004004i−4i4i−4i-44-44i−4i4i−4i004-40000000000000004i−4i00000000000000000000000000000000000000000
χ624-44-44-400400−4i4i−4i4i-44-4−4i4i−4i4i004-4000000000000000−4i4i00000000000000000000000000000000000000000
χ634-44-44-400-2004i−4i4i−4i2-22−2i2i−2i2i00-22000000000000000−2i2i06−66−66−66−6i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ644-44-44-400-2004i−4i4i−4i2-22−2i2i−2i2i00-22000000000000000−2i2i0−66−66−66−66−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ654-44-44-400-200−4i4i−4i4i2-222i−2i2i−2i00-220000000000000002i−2i06−66−66−66−6−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ664-44-44-400-200−4i4i−4i4i2-222i−2i2i−2i00-220000000000000002i−2i0−66−66−66−66i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ674-44-4-44004004i−4i−4i4i-44-44i−4i4i−4i00-44000000000000000−4i4i00000000000000000000000000000000000000000
χ684-44-4-4400400−4i4i4i−4i-44-4−4i4i−4i4i00-440000000000000004i−4i00000000000000000000000000000000000000000
χ694-44-4-4400-2004i−4i−4i4i2-22−2i2i−2i2i002-20000000000000002i−2i06−66−6−66−66−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ704-44-4-4400-2004i−4i−4i4i2-22−2i2i−2i2i002-20000000000000002i−2i0−66−666−66−6i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ714-44-4-4400-200−4i4i4i−4i2-222i−2i2i−2i002-2000000000000000−2i2i06−66−6−66−66i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ724-44-4-4400-200−4i4i4i−4i2-222i−2i2i−2i002-2000000000000000−2i2i0−66−666−66−6−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ734-4-44000044-40000-4-440000000000004i−4i00000040000-44i−4i−4i4i000000000000000000000000000000000000
χ744-4-44000044-40000-4-44000000000000−4i4i00000040000-4−4i4i4i−4i000000000000000000000000000000000000
χ754-4-4400004-440000-4-4400000000000000004-400-400004000000004-4-440000000000000000000000000000
χ764-4-4400004-440000-4-440000000000000000-4400-40000400000000-444-40000000000000000000000000000
χ774-4-440000-24-4000022-2−2i32i32i3−2i3000000−2i32i34i−4i000000-200002−2i2i2i−2i0000000023−23−2323000000000000000000000000
χ784-4-440000-24-4000022-2−2i32i32i3−2i3000000−2i32i3−4i4i000000-2000022i−2i−2i2i00000000−232323−23000000000000000000000000
χ794-4-440000-24-4000022-22i3−2i3−2i32i30000002i3−2i34i−4i000000-200002−2i2i2i−2i00000000−232323−23000000000000000000000000
χ804-4-440000-24-4000022-22i3−2i3−2i32i30000002i3−2i3−4i4i000000-2000022i−2i−2i2i0000000023−23−2323000000000000000000000000
χ814-4-440000-2-44000022-2−2i32i32i3−2i30000002i3−2i300004-40020000-200002i3−2i3−2i32i3-222-20000000000000000000000000000
χ824-4-440000-2-44000022-2−2i32i32i3−2i30000002i3−2i30000-440020000-20000−2i32i32i3−2i32-2-220000000000000000000000000000
χ834-4-440000-2-44000022-22i3−2i3−2i32i3000000−2i32i300004-40020000-20000−2i32i32i3−2i3-222-20000000000000000000000000000
χ844-4-440000-2-44000022-22i3−2i3−2i32i3000000−2i32i30000-440020000-200002i3−2i3−2i32i32-2-220000000000000000000000000000

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