Finite Group Databasebeta

← Group #10829793

Character table — Group #10829793

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order122222344444466612121212444661212121212122244444488881212121212121212121224242424242424244444661212244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111-1-111111111111-1-1-111-1-1-1-1111-11-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-11-1
χ101111111-1-111111111111-1-1-111-1-1-1-1111-11-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-11
χ111111111-1-111111111111-1-1-111-1-1-1-1111-11-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111111-11-1-1-1-1-111-1-111-11
χ121111111-1-111111111111-1-1-111-1-1-1-1111-11-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-111-1-11-1
χ131111111-1-111111111111-1-1-111-1-1-1-111-11-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-111111-1
χ141111111-1-111111111111-1-1-111-1-1-1-111-11-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11111111-1-1-1-1-11
χ151111111-1-111111111111-1-1-111-1-1-1-111-11-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-11-1-111-1-111-1-1-11
χ161111111-1-111111111111-1-1-111-1-1-1-111-11-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1111-1
χ17222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000000002-200000000000000000000000000002-22-20000
χ18222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000000002-20000000000000000000000000000-22-220000
χ192222222-2-2-2-2-2-2222-2-2-2-2-22222-2-222-2-2000000000000-2200000000000000000000000000002-2-220000
χ202222222-2-2-2-2-2-2222-2-2-2-2-22222-2-222-2-2000000000000-220000000000000000000000000000-222-20000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-1000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100001111000000000000
χ25222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-11111-1-12-22-222-2-222-2-211-1-1-1-11111-1-1-1-111110000-11-11000000000000
χ26222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-11111-1-12-22-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-11-11000000000000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-11111-1-1-22-2222-2-2-2-22211-1-1-1-111111111-1-1-1-100001-11-1000000000000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-11111-1-1-22-22-2-22222-2-2111111-1-1-1-1-1-1-1-1111100001-11-1000000000000
χ292222-2-22222-2-22222-2-2-2-2-22-2-2-222-2-22222-2-200000000-220000000000000000000022-2-2000000000000
χ302222-2-22222-2-22222-2-2-2-2-22-2-2-222-2-222-2-22200000000-2200000000000000000000-2-222000000000000
χ312222-2-2222-222-22222222-2-22-2-22222-2-2000000000000-2-2000000000000000022-2-200002-20000000000
χ322222-2-2222-222-22222222-2-22-2-22222-2-2000000000000-2-20000000000000000-2-2220000-220000000000
χ332222-2-22-2-22-2-22222-2-2-2-22-22-2-2-2-222222-2-22000000002-2000000000000000000002-2-22000000000000
χ342222-2-22-2-22-2-22222-2-2-2-22-22-2-2-2-22222-222-2000000002-200000000000000000000-222-2000000000000
χ352222-2-22-2-2-222-2222222222-2-2-2-2-2-2-2-2-200000000000022000000000000000022-2-20000-220000000000
χ362222-2-22-2-2-222-2222222222-2-2-2-2-2-2-2-2-2000000000000220000000000000000-2-22200002-20000000000
χ372222-2-2-1222-2-22-1-1-11111-22-211-1-111-1-122-2-2000000001-133−3−333−3−333−3−333−3−30000-1-111000000000000
χ382222-2-2-1222-2-22-1-1-11111-22-211-1-111-1-122-2-2000000001-1−3−333−3−333−3−333−3−3330000-1-111000000000000
χ392222-2-2-1222-2-22-1-1-11111-22-211-1-111-1-1-2-222000000001-133−3−333−3−3−3−333−3−333000011-1-1000000000000
χ402222-2-2-1222-2-22-1-1-11111-22-211-1-111-1-1-2-222000000001-1−3−333−3−33333−3−333−3−3000011-1-1000000000000
χ412222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-12-2-2200000000-1133−3−3−3−33333−3−3−3−3330000-111-1000000000000
χ422222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-12-2-2200000000-11−3−33333−3−3−3−33333−3−30000-111-1000000000000
χ432222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-1-222-200000000-1133−3−3−3−333−3−33333−3−300001-1-11000000000000
χ442222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-1-222-200000000-11−3−33333−3−333−3−3−3−33300001-1-11000000000000
χ452-22-22-2200-22-22-2-2222-2-20002-200002-2000000002i−2i0000000000002i−2i2i−2i00002i−2i2i−2i0000002-200000000
χ462-22-22-2200-22-22-2-2222-2-20002-200002-2000000002i−2i0000000000002i−2i2i−2i0000−2i2i−2i2i000000-2200000000
χ472-22-22-2200-22-22-2-2222-2-20002-200002-200000000−2i2i000000000000−2i2i−2i2i00002i−2i2i−2i000000-2200000000
χ482-22-22-2200-22-22-2-2222-2-20002-200002-200000000−2i2i000000000000−2i2i−2i2i0000−2i2i−2i2i0000002-200000000
χ492-22-2-2220022-2-2-2-2222-2-2000-220000-2200000000002-2000000000000002-22-22i−2i−2i2i0000000000002i−2i00
χ502-22-2-2220022-2-2-2-2222-2-2000-220000-2200000000002-2000000000000002-22-2−2i2i2i−2i000000000000−2i2i00
χ512-22-2-2220022-2-2-2-2222-2-2000-220000-220000000000-2200000000000000-22-222i−2i−2i2i000000000000−2i2i00
χ522-22-2-2220022-2-2-2-2222-2-2000-220000-220000000000-2200000000000000-22-22−2i2i2i−2i0000000000002i−2i00
χ53444444-244-4-4-4-4-2-2-222224-4-4-2-2-2-22222000000000000-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-22222-444-2-222-2-2220000000000002-2000000000000000000000000000000000000
χ554444-4-4-244-444-4-2-2-2-2-2-2-2-4-4422-2-2-2-22200000000000022000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-2-2-2-2-244-422222222000000000000-2-2000000000000000000000000000000000000
χ5744-4-40044-400004-4-40000000004-4000000002-22-20000002-22-22-22-20000000000000000000000000000
χ5844-4-40044-400004-4-40000000004-400000000-22-22000000-22-22-22-220000000000000000000000000000
χ5944-4-4004-4400004-4-4000000000-44000000002-2-220000002-22-2-22-220000000000000000000000000000
χ6044-4-4004-4400004-4-4000000000-4400000000-222-2000000-22-222-22-20000000000000000000000000000
χ6144-4-400-24-40000-22223−2323−2300000-2223−230000002-22-2000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000000000
χ6244-4-400-24-40000-22223−2323−2300000-2223−23000000-22-220000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000000000
χ6344-4-400-24-40000-222−2323−232300000-22−23230000002-22-2000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000000000
χ6444-4-400-24-40000-222−2323−232300000-22−2323000000-22-220000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000000000
χ6544-4-400-2-440000-22223−2323−23000002-2−23230000002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000000000
χ6644-4-400-2-440000-22223−2323−23000002-2−2323000000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000000000
χ6744-4-400-2-440000-222−2323−2323000002-223−230000002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000000000
χ6844-4-400-2-440000-222−2323−2323000002-223−23000000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000000000
χ694-44-44-44004-44-4-4-44-4-4440004-40000-4400000000000000000000000000000000000000000000000000
χ704-44-44-4-2004-44-422-222-2-2000-2200002-20000000000000000000000000023−23−232300000000000000000000
χ714-44-44-4-2004-44-422-222-2-2000-2200002-200000000000000000000000000−232323−2300000000000000000000
χ724-44-44-4-200-44-4422-2-2-222000-220000-22000000004i−4i000000000000−2i2i−2i2i000000000000000000000000
χ734-44-44-4-200-44-4422-2-2-222000-220000-2200000000−4i4i0000000000002i−2i2i−2i000000000000000000000000
χ744-44-4-44400-4-444-4-44-4-444000-4400004-400000000000000000000000000000000000000000000000000
χ754-44-4-44-20044-4-422-2-2-2220002-200002-200000000004-400000000000000-22-2200000000000000000000
χ764-44-4-44-20044-4-422-2-2-2220002-200002-20000000000-44000000000000002-22-200000000000000000000
χ774-44-4-44-200-4-44422-222-2-20002-20000-220000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ784-44-4-44-200-4-44422-222-2-20002-20000-2200000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ798-8-88008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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