Finite Group Databasebeta

← Group #10855241

Character table — Group #10855241

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222222234444444466666664444441212121212121212448888121212121212121212122424242424242424444488888888246612122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1
χ5111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-111
χ91111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-11-1-11111111-1-1-1-1-1
χ101111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1-1-1-111111
χ111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-111-1-1-1-111111-1-1-1
χ121111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-111-1-111-1-1-1-1-1111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-11-1-111-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-111-1-111-111-1-11-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111111-1-1-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-11-1-111-1-1-111111-1-1
χ17222222222-22222-2-2-222222220000-2-22222-2-2-2-2000000-2-2000000000000000022220000000000000000-20000-200
χ18222222222-22222-2-2-222222220000-2-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000000000000020000200
χ19222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000022000000000000000022-2-20000000000000000-20000200
χ20222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000220000000000000000-2-222000000000000000020000-200
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-222-2-211-1-1-1-11111-1-1-1-11111000000000000-2211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-22211-1-1-1-111111111-1-1-1-10000000000002-2-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2111111-1-1-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-222111111-1-1-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ292222-2-2-2-22-200002-222-2-2-222-222-2-2000000-2-2220000000022-2-200000000000000002i2i−2i−2i0000000000000002i−2i000
χ302222-2-2-2-22-200002-222-2-2-222-222-2-2000000-2-2220000000022-2-20000000000000000−2i−2i2i2i000000000000000−2i2i000
χ312222-2-2-2-22-200002-222-2-2-222-2-2-222000000-2-22200000000-2-22200000000000000002i2i−2i−2i000000000000000−2i2i000
χ322222-2-2-2-22-200002-222-2-2-222-2-2-222000000-2-22200000000-2-2220000000000000000−2i−2i2i2i0000000000000002i−2i000
χ332-22-22-22-22022-2-2000-22-222-2-200000022-2-2000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i22-22-2−i2i2−i2i2−i2−i2i2i20000000000000000
χ342-22-22-22-22022-2-2000-22-222-2-200000022-2-2000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2-22-22i2−i2i2−i2i2i2−i2−i20000000000000000
χ352-22-22-22-22022-2-2000-22-222-2-200000022-2-2000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i22-22-2i2−i2i2−i2i2i2−i2−i20000000000000000
χ362-22-22-22-22022-2-2000-22-222-2-200000022-2-2000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2-22-22−i2i2−i2i2−i2−i2i2i20000000000000000
χ372-22-22-22-220-2-222000-22-222-2-2000000-2-222000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i22-2-22i2−i2i2−i2−i2−i2i2i20000000000000000
χ382-22-22-22-220-2-222000-22-222-2-2000000-2-222000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2-222-2−i2i2−i2i2i2i2−i2−i20000000000000000
χ392-22-22-22-220-2-222000-22-222-2-2000000-2-222000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i22-2-22−i2i2−i2i2i2i2−i2−i20000000000000000
χ402-22-22-22-220-2-222000-22-222-2-2000000-2-222000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2-222-2i2−i2i2−i2−i2−i2i2i20000000000000000
χ412-2-2222-2-2222i−2i2i−2i-2-22-222-2-22-22-22-22i−2i2i−2i2i−2i2-22-22i−2i00002i−2i2-22-22i2i−2i−2i000000000000000000000000000000000000
χ422-2-2222-2-2222i−2i2i−2i-2-22-222-2-22-2-22-222i−2i2i−2i2i−2i2-22-2−2i2i00002i−2i-22-22−2i−2i2i2i000000000000000000000000000000000000
χ432-2-2222-2-222−2i2i−2i2i-2-22-222-2-22-22-22-2−2i2i−2i2i−2i2i2-22-2−2i2i0000−2i2i2-22-2−2i−2i2i2i000000000000000000000000000000000000
χ442-2-2222-2-222−2i2i−2i2i-2-22-222-2-22-2-22-22−2i2i−2i2i−2i2i2-22-22i−2i0000−2i2i-22-222i2i−2i−2i000000000000000000000000000000000000
χ452-2-2222-2-22-22i−2i2i−2i22-2-222-2-22-20000−2i2i2i−2i2i−2i-22-22000000−2i2i00000000000000000000000000000000000002-20002i−2i
χ462-2-2222-2-22-22i−2i2i−2i22-2-222-2-22-20000−2i2i2i−2i2i−2i-22-22000000−2i2i0000000000000000000000000000000000000-22000−2i2i
χ472-2-2222-2-22-2−2i2i−2i2i22-2-222-2-22-200002i−2i−2i2i−2i2i-22-220000002i−2i00000000000000000000000000000000000002-2000−2i2i
χ482-2-2222-2-22-2−2i2i−2i2i22-2-222-2-22-200002i−2i−2i2i−2i2i-22-220000002i−2i0000000000000000000000000000000000000-220002i−2i
χ492-2-2222-2-2-122i−2i2i−2i-2-221-1-111-112-22-22i−2i−ii−ii-11-112i−2i0000−ii-11-11−i−iii3−33−3−i3i3−i3i300000000000000−i3i33−30000000000
χ502-2-2222-2-2-122i−2i2i−2i-2-221-1-111-112-22-22i−2i−ii−ii-11-112i−2i0000−ii-11-11−i−iii−33−33i3−i3i3−i300000000000000i3−i3−330000000000
χ512-2-2222-2-2-122i−2i2i−2i-2-221-1-111-11-22-222i−2i−ii−ii-11-11−2i2i0000−ii1-11-1ii−i−i3−33−3−i3i3−i3i300000000000000i3−i3−330000000000
χ522-2-2222-2-2-122i−2i2i−2i-2-221-1-111-11-22-222i−2i−ii−ii-11-11−2i2i0000−ii1-11-1ii−i−i−33−33i3−i3i3−i300000000000000−i3i33−30000000000
χ532-2-2222-2-2-12−2i2i−2i2i-2-221-1-111-112-22-2−2i2ii−ii−i-11-11−2i2i0000i−i-11-11ii−i−i3−33−3i3−i3i3−i300000000000000i3−i33−30000000000
χ542-2-2222-2-2-12−2i2i−2i2i-2-221-1-111-112-22-2−2i2ii−ii−i-11-11−2i2i0000i−i-11-11ii−i−i−33−33−i3i3−i3i300000000000000−i3i3−330000000000
χ552-2-2222-2-2-12−2i2i−2i2i-2-221-1-111-11-22-22−2i2ii−ii−i-11-112i−2i0000i−i1-11-1−i−iii3−33−3i3−i3i3−i300000000000000−i3i3−330000000000
χ562-2-2222-2-2-12−2i2i−2i2i-2-221-1-111-11-22-22−2i2ii−ii−i-11-112i−2i0000i−i1-11-1−i−iii−33−33−i3i3−i3i300000000000000i3−i33−30000000000
χ572-2-22-2-2222-20000-222-2-2-22-2222-2-22000000-222-2000000002-2-22000000000000000000002-22-20000002-200000000
χ582-2-22-2-2222-20000-222-2-2-22-2222-2-22000000-222-2000000002-2-2200000000000000000000-22-22000000-2200000000
χ592-2-22-2-2222-20000-222-2-2-22-222-222-2000000-222-200000000-222-2000000000000000000002-22-2000000-2200000000
χ602-2-22-2-2222-20000-222-2-2-22-222-222-2000000-222-200000000-222-200000000000000000000-22-220000002-200000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-20000-4-4-2-2-2-222220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200004422222222000000-2-200000000000000000000000000000000000000000000
χ634444-4-4-4-4440000-44-44-4-4-444-4000000000044-4-40000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-240000-44-4-2222-2-220000000000-2-22200000000000023−2323−23000000000000000000000000000000000000
χ654444-4-4-4-4-240000-44-4-2222-2-220000000000-2-222000000000000−2323−2323000000000000000000000000000000000000
χ664444-4-4-4-4-2-400004-44-2222-2-2244-4-400000022-2-200000000-2-2220000000000000000000000000000000000000000
χ674444-4-4-4-4-2-400004-44-2222-2-22-4-44400000022-2-20000000022-2-20000000000000000000000000000000000000000
χ6844-4-44-4-44404i−4i−4i4i00044-4-4-4-440000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6944-4-44-4-4440−4i4i4i−4i00044-4-4-4-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-44-204i−4i−4i4i000-2-22222-2000000−2i2i2i−2i00000000000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ7144-4-44-4-44-204i−4i−4i4i000-2-22222-2000000−2i2i2i−2i00000000000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ7244-4-44-4-44-20−4i4i4i−4i000-2-22222-20000002i−2i−2i2i00000000000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ7344-4-44-4-44-20−4i4i4i−4i000-2-22222-20000002i−2i−2i2i00000000000000000000−i6i6i6−i66−6−660000000000000000000000000000
χ7444-4-4-444-44000000004-444-4-4-40000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ7544-4-4-444-44000000004-444-4-4-400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ764-44-44-44-4-2044-4-40002-22-2-222000000-2-222000000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ774-44-44-44-4-2044-4-40002-22-2-222000000-2-2220000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ784-44-44-44-4-20-4-4440002-22-2-22200000022-2-2000000−2i22i22i2−2i20000000000i2i2−i2−i2−i2−i2i2i20000000000000000000000000000
χ794-44-44-44-4-20-4-4440002-22-2-22200000022-2-20000002i2−2i2−2i22i20000000000−i2−i2i2i2i2i2−i2−i20000000000000000000000000000
χ804-44-4-44-44400000000-4-44-44-4400000000000000000000000000000000000000000022−22−222200000000000000000000
χ814-44-4-44-44400000000-4-44-44-44000000000000000000000000000000000000000000−222222−2200000000000000000000
χ824-4-4444-4-4-2-44i−4i4i−4i44-42-2-222-220000−4i4i−2i2i−2i2i2-22-20000002i−2i00000000000000000000000000000000000000000000
χ834-4-4444-4-4-2-4−4i4i−4i4i44-42-2-222-2200004i−4i2i−2i2i−2i2-22-2000000−2i2i00000000000000000000000000000000000000000000
χ844-4-44-4-4444400004-4-4-4-4-44-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-2400004-4-4222-22-2-20000000000-222-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ864-4-44-4-444-2400004-4-4222-22-2-20000000000-222-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ874-4-44-4-444-2-40000-444222-22-2-24-4-440000002-2-2200000000-222-20000000000000000000000000000000000000000
χ884-4-44-4-444-2-40000-444222-22-2-2-444-40000002-2-22000000002-2-220000000000000000000000000000000000000000
χ8988-8-8-888-8-400000000-44-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-40000000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000

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