Finite Group Databasebeta

← Group #10855265

Character table — Group #10855265

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
χ5111111111111111111111111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-111-1-1-1-1-11111-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-111-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111111-1-111111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111-1-111-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-1111-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-111-1-11-1-111-1-1-1-11
χ17222222222-2-2-2-2222222200002200002222-2-2-2-2222200-20000-2-2000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-2222222200002200002222-2-2-2-2-2-2-2-200-20000-2-20000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200200002200000000000000002222000000000-2000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-222221111-1-1-1-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-10000-2-2-2-2-222111111-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-1000022-2222211-1-1-1-111111111-1-1-1-100000000-2-1-1110000000000
χ2922-222-2-2-22-222-222-2-2-2-2222-2-200000000002-2-220000000000000000022-2-20000000000002i2i−2i−2i00000000002i−2i000
χ3022-222-2-2-22-222-222-2-2-2-2222-2-200000000002-2-220000000000000000022-2-2000000000000−2i−2i2i2i0000000000−2i2i000
χ3122-222-2-2-22-222-222-2-2-2-22-2-22200000000002-2-2200000000000000000-2-2220000000000002i2i−2i−2i0000000000−2i2i000
χ3222-222-2-2-22-222-222-2-2-2-22-2-22200000000002-2-2200000000000000000-2-222000000000000−2i−2i2i2i00000000002i−2i000
χ3322-2-2-22-22200002-22-2-22-200002i−2i−i2−i2i2i22i2i−2i−2i000022-2-2000002−20000000000−i2−i2i2i222−2−22i−2i00−i2i2−i2i20000000000002−20
χ3422-2-2-22-22200002-22-2-22-200002i−2i−i2−i2i2i22i2i−2i−2i0000-2-222000002−20000000000−i2−i2i2i222−2−2−2i2i00i2−i2i2−i2000000000000−220
χ3522-2-2-22-22200002-22-2-22-200002i−2ii2i2−i2−i22i2i−2i−2i000022-2-200000−220000000000i2i2−i2−i2−2−2222i−2i00i2−i2i2−i2000000000000−220
χ3622-2-2-22-22200002-22-2-22-200002i−2ii2i2−i2−i22i2i−2i−2i0000-2-22200000−220000000000i2i2−i2−i2−2−222−2i2i00−i2i2−i2i20000000000002−20
χ3722-2-2-22-22200002-22-2-22-20000−2i2i−i2−i2i2i2−2i−2i2i2i000022-2-200000−220000000000−i2−i2i2i2−2−222−2i2i00−i2i2−i2i2000000000000−220
χ3822-2-2-22-22200002-22-2-22-20000−2i2i−i2−i2i2i2−2i−2i2i2i0000-2-22200000−220000000000−i2−i2i2i2−2−2222i−2i00i2−i2i2−i20000000000002−20
χ3922-2-2-22-22200002-22-2-22-20000−2i2ii2i2−i2−i2−2i−2i2i2i000022-2-2000002−20000000000i2i2−i2−i222−2−2−2i2i00i2−i2i2−i20000000000002−20
χ4022-2-2-22-22200002-22-2-22-20000−2i2ii2i2−i2−i2−2i−2i2i2i0000-2-222000002−20000000000i2i2−i2−i222−2−22i−2i00−i2i2−i2i2000000000000−220
χ412-222-22-2-2222-2-2-2-222-2-222-22-20000000000-22-222i−2i2i−2i00000000000002-22-200000000002i−2i0000000000002i−2i00000
χ422-222-22-2-2222-2-2-2-222-2-222-22-20000000000-22-22−2i2i−2i2i00000000000002-22-20000000000−2i2i000000000000−2i2i00000
χ432-222-22-2-2222-2-2-2-222-2-22-22-220000000000-22-222i−2i2i−2i0000000000000-22-2200000000002i−2i000000000000−2i2i00000
χ442-222-22-2-2222-2-2-2-222-2-22-22-220000000000-22-22−2i2i−2i2i0000000000000-22-220000000000−2i2i0000000000002i−2i00000
χ452-222-22-2-22-2-222-2-222-2-22000000000000002-22-22i−2i2i−2i0002i−2i00002i2i−2i−2i00000000000000−2i2i00000000002-20000000
χ462-222-22-2-22-2-222-2-222-2-22000000000000002-22-22i−2i2i−2i000−2i2i0000−2i−2i2i2i00000000000000−2i2i0000000000-220000000
χ472-222-22-2-22-2-222-2-222-2-22000000000000002-22-2−2i2i−2i2i0002i−2i00002i2i−2i−2i000000000000002i−2i0000000000-220000000
χ482-222-22-2-22-2-222-2-222-2-22000000000000002-22-2−2i2i−2i2i000−2i2i0000−2i−2i2i2i000000000000002i−2i00000000002-20000000
χ492-2-22-2-2222-22-22-2-2-2-22222-2-22002-22-20000-2-22200002-2000000000002-2-222-22-200000000000002-2000000000000
χ502-2-22-2-2222-22-22-2-2-2-22222-2-2200-22-220000-2-2220000-22000000000002-2-22-22-220000000000000-22000000000000
χ512-2-22-2-2222-22-22-2-2-2-2222-222-2002-22-20000-2-2220000-2200000000000-222-22-22-20000000000000-22000000000000
χ522-2-22-2-2222-22-22-2-2-2-2222-222-200-22-220000-2-22200002-200000000000-222-2-22-2200000000000002-2000000000000
χ532-2-22-2-222-1-22-221111-1-1-12-2-22002-22-2−i3i3−i3i311-1-100002-200000−i3i3−i3i3−i3i3-111-1-11-11−i3i3−i3i3000000000-11−i3i30000000000
χ542-2-22-2-222-1-22-221111-1-1-12-2-22002-22-2i3−i3i3−i311-1-100002-200000i3−i3i3−i3i3−i3-111-1-11-11i3−i3i3−i3000000000-11i3−i30000000000
χ552-2-22-2-222-1-22-221111-1-1-12-2-2200-22-22−i3i3−i3i311-1-10000-2200000−i3i3−i3i3−i3i3-111-11-11-1i3−i3i3−i30000000001-1i3−i30000000000
χ562-2-22-2-222-1-22-221111-1-1-12-2-2200-22-22i3−i3i3−i311-1-10000-2200000i3−i3i3−i3i3−i3-111-11-11-1−i3i3−i3i30000000001-1−i3i30000000000
χ572-2-22-2-222-1-22-221111-1-1-1-222-2002-22-2−i3i3−i3i311-1-10000-2200000−i3i3i3−i3i3−i31-1-11-11-11−i3i3−i3i30000000001-1i3−i30000000000
χ582-2-22-2-222-1-22-221111-1-1-1-222-2002-22-2i3−i3i3−i311-1-10000-2200000i3−i3−i3i3−i3i31-1-11-11-11i3−i3i3−i30000000001-1−i3i30000000000
χ592-2-22-2-222-1-22-221111-1-1-1-222-200-22-22−i3i3−i3i311-1-100002-200000−i3i3i3−i3i3−i31-1-111-11-1i3−i3i3−i3000000000-11−i3i30000000000
χ602-2-22-2-222-1-22-221111-1-1-1-222-200-22-22i3−i3i3−i311-1-100002-200000i3−i3−i3i3−i3i31-1-111-11-1−i3i3−i3i3000000000-11i3−i30000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000-2-2-2-22222000000-4000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-400002222222200000040000-2-2000000000000000000000000000000000000000
χ63444-4-4-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ64444-4-4-44-4400004-4-444-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6544-444-4-4-444-4-4444-4-4-4-4400000000000000-444-40000000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-24-4-44-2-22222-2000000000000002-2-22000000000000023−23−232300000000000000000000000000000000000
χ6744-444-4-4-4-24-4-44-2-22222-2000000000000002-2-220000000000000−232323−2300000000000000000000000000000000000
χ6844-444-4-4-4-2-444-4-2-22222-244-4-40000000000-222-200000000000000000-2-2220000000000000000000000000000000
χ6944-444-4-4-4-2-444-4-2-22222-2-4-4440000000000-222-20000000000000000022-2-20000000000000000000000000000000
χ7044-4-4-44-44-20000-22-222-2200004i−4i−2i2−2i22i22i2−2i−2i2i2i000000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ7144-4-4-44-44-20000-22-222-2200004i−4i2i22i2−2i2−2i2−2i−2i2i2i0000000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ7244-4-4-44-44-20000-22-222-220000−4i4i−2i2−2i22i22i22i2i−2i−2i0000000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ7344-4-4-44-44-20000-22-222-220000−4i4i2i22i2−2i2−2i22i2i−2i−2i000000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ744-444-44-4-4-244-4-422-2-222-24-44-400000000002-22-200000000000000000-22-220000000000000000000000000000000
χ754-444-44-4-4-244-4-422-2-222-2-44-4400000000002-22-2000000000000000002-22-20000000000000000000000000000000
χ764-444-44-4-4-2-4-44422-2-222-200000000000000-22-2200000004i−4i0000−2i−2i2i2i00000000000000000000000000000000000
χ774-444-44-4-4-2-4-44422-2-222-200000000000000-22-220000000−4i4i00002i2i−2i−2i00000000000000000000000000000000000
χ784-44-44-4-4440000-44-44-44-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ794-44-44-4-4440000-44-44-44-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ804-44-44-4-44-200002-22-22-22000000−2i22i22i2−2i223−23−23230000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ814-44-44-4-44-200002-22-22-22000000−2i22i22i2−2i2−232323−230000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ824-44-44-4-44-200002-22-22-220000002i2−2i2−2i22i223−23−23230000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ834-44-44-4-44-200002-22-22-220000002i2−2i2−2i22i2−232323−230000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ844-4-44-4-44444-44-4-4-4-4-44440000000000000044-4-40000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-44-42222-2-2-20000000000−2i32i3−2i32i3-2-222000000000002i3−2i3000000000000000000000000000000000000000
χ864-4-44-4-444-24-44-42222-2-2-200000000002i3−2i32i3−2i3-2-22200000000000−2i32i3000000000000000000000000000000000000000
χ874-4-4-4444-440000-444-44-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ884-4-4-4444-440000-444-44-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ89888-8-8-88-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8888-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000

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