Finite Group Databasebeta

← Group #10855310

Character table — Group #10855310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666662222448888121212121212121244444444466668812121212121224242424242424244444888826612124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-11111111-1-1-1-11111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1111-1-111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-2222200-200000000-2-200000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-200-200000000-2-2000000000000-2-2220000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200200000000220000000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-21111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-10000-2-2-2221111-2-211-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-1000022-22211112211-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-22-2-2-22-222-222-2-2-22-222-2-20000002-2-20000200000000022-2-2000000000000000000002i2i−2i−2i00000000002i−2i000
χ30222-22-2-2-22-222-222-2-2-22-222-2-20000002-2-20000200000000022-2-200000000000000000000−2i−2i2i2i0000000000−2i2i000
χ31222-22-2-2-22-222-222-2-2-22-2-2-2220000002-2-200002000000000-2-222000000000000000000002i2i−2i−2i0000000000−2i2i000
χ32222-22-2-2-22-222-222-2-2-22-2-2-2220000002-2-200002000000000-2-22200000000000000000000−2i−2i2i2i00000000002i−2i000
χ332-222-22-2-2222-2-2-2-222-22-22-22-2000000-22-2000022i2i−2i−2i000002-22-20000000000000000002i−2i0000000000002i−2i00000
χ342-222-22-2-2222-2-2-2-222-22-22-22-2000000-22-200002−2i−2i2i2i000002-22-2000000000000000000−2i2i000000000000−2i2i00000
χ352-222-22-2-2222-2-2-2-222-22-2-22-22000000-22-2000022i2i−2i−2i00000-22-220000000000000000002i−2i000000000000−2i2i00000
χ362-222-22-2-2222-2-2-2-222-22-2-22-22000000-22-200002−2i−2i2i2i00000-22-22000000000000000000−2i2i0000000000002i−2i00000
χ372-222-22-2-22-2-222-2-222-22-200000000002-220000-22i2i−2i−2i0002i−2i000000002i2i−2i−2i0000000000−2i2i00000000002-20000000
χ382-222-22-2-22-2-222-2-222-22-200000000002-220000-22i2i−2i−2i000−2i2i00000000−2i−2i2i2i0000000000−2i2i0000000000-220000000
χ392-222-22-2-22-2-222-2-222-22-200000000002-220000-2−2i−2i2i2i0002i−2i000000002i2i−2i−2i00000000002i−2i0000000000-220000000
χ402-222-22-2-22-2-222-2-222-22-200000000002-220000-2−2i−2i2i2i000−2i2i00000000−2i−2i2i2i00000000002i−2i00000000002-20000000
χ412-22-2-2-2222-22-22-2-2-2-22222-2-220022-2-2-2-220000200002-20002-2-220000000022-2-20000000000000002-20000000000
χ422-22-2-2-2222-22-22-2-2-2-22222-2-2200-2-222-2-22000020000-220002-2-2200000000-2-222000000000000000-220000000000
χ432-22-2-2-2222-22-22-2-2-2-2222-222-20022-2-2-2-22000020000-22000-222-20000000022-2-2000000000000000-220000000000
χ442-22-2-2-2222-22-22-2-2-2-2222-222-200-2-222-2-220000200002-2000-222-200000000-2-2220000000000000002-20000000000
χ452-22-2-2-222-1-22-221111-1-1-12-2-220022-2-211-1−i3−i3i3i3-100002-2000-111-100−i3i3−i3i3−i3i3-1-111−i3−i3i3i3000000000−i3i3-110000000000
χ462-22-2-2-222-1-22-221111-1-1-12-2-220022-2-211-1i3i3−i3−i3-100002-2000-111-100i3−i3i3−i3i3−i3-1-111i3i3−i3−i3000000000i3−i3-110000000000
χ472-22-2-2-222-1-22-221111-1-1-12-2-2200-2-22211-1−i3−i3i3i3-10000-22000-111-100−i3i3−i3i3−i3i311-1-1i3i3−i3−i3000000000i3−i31-10000000000
χ482-22-2-2-222-1-22-221111-1-1-12-2-2200-2-22211-1i3i3−i3−i3-10000-22000-111-100i3−i3i3−i3i3−i311-1-1−i3−i3i3i3000000000−i3i31-10000000000
χ492-22-2-2-222-1-22-221111-1-1-1-222-20022-2-211-1−i3−i3i3i3-10000-220001-1-1100−i3i3i3−i3i3−i3-1-111−i3−i3i3i3000000000i3−i31-10000000000
χ502-22-2-2-222-1-22-221111-1-1-1-222-20022-2-211-1i3i3−i3−i3-10000-220001-1-1100i3−i3−i3i3−i3i3-1-111i3i3−i3−i3000000000−i3i31-10000000000
χ512-22-2-2-222-1-22-221111-1-1-1-222-200-2-22211-1−i3−i3i3i3-100002-20001-1-1100−i3i3i3−i3i3−i311-1-1i3i3−i3−i3000000000−i3i3-110000000000
χ522-22-2-2-222-1-22-221111-1-1-1-222-200-2-22211-1i3i3−i3−i3-100002-20001-1-1100i3−i3−i3i3−i3i311-1-1−i3−i3i3i3000000000i3−i3-110000000000
χ532-2-222-22-2200002-22-22-2-200002i−2i−i2i2−i2i20002i−2i2i−2i02-22-20000000002−2000000−i2i2−i2i22−22−22i−2i00−i2i2−i2i20000000000002−20
χ542-2-222-22-2200002-22-22-2-200002i−2i−i2i2−i2i20002i−2i2i−2i0-22-220000000002−2000000−i2i2−i2i22−22−2−2i2i00i2−i2i2−i2000000000000−220
χ552-2-222-22-2200002-22-22-2-200002i−2ii2−i2i2−i20002i−2i2i−2i02-22-2000000000−22000000i2−i2i2−i2−22−222i−2i00i2−i2i2−i2000000000000−220
χ562-2-222-22-2200002-22-22-2-200002i−2ii2−i2i2−i20002i−2i2i−2i0-22-22000000000−22000000i2−i2i2−i2−22−22−2i2i00−i2i2−i2i20000000000002−20
χ572-2-222-22-2200002-22-22-2-20000−2i2i−i2i2−i2i2000−2i2i−2i2i02-22-2000000000−22000000−i2i2−i2i2−22−22−2i2i00−i2i2−i2i2000000000000−220
χ582-2-222-22-2200002-22-22-2-20000−2i2i−i2i2−i2i2000−2i2i−2i2i0-22-22000000000−22000000−i2i2−i2i2−22−222i−2i00i2−i2i2−i20000000000002−20
χ592-2-222-22-2200002-22-22-2-20000−2i2ii2−i2i2−i2000−2i2i−2i2i02-22-20000000002−2000000i2−i2i2−i22−22−2−2i2i00i2−i2i2−i20000000000002−20
χ602-2-222-22-2200002-22-22-2-20000−2i2ii2−i2i2−i2000−2i2i−2i2i0-22-220000000002−2000000i2−i2i2−i22−22−22i−2i00−i2i2−i2i2000000000000−220
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-22000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000400000000-2-200000000000000000000000000000000000
χ63444-44-4-4-444-4-4444-4-4-44-40000000000-4440000-40000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-24-4-44-2-2222-2200000000002-2-2000020000000000000000023−23−23230000000000000000000000000000000
χ65444-44-4-4-4-24-4-44-2-2222-2200000000002-2-20000200000000000000000−232323−230000000000000000000000000000000
χ66444-44-4-4-4-2-444-4-2-2222-2244-4-4000000-2220000-2000000000-2-222000000000000000000000000000000000000000
χ67444-44-4-4-4-2-444-4-2-2222-22-4-444000000-2220000-200000000022-2-2000000000000000000000000000000000000000
χ6844-44-4-4-4440000-444-4-4-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6944-44-4-4-4440000-444-4-4-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ7044-4-4-444-440000-44-444-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ7144-4-4-444-440000-44-444-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ7244-4-4-444-4-200002-22-2-222000000−2i22i22i2−2i200023−23−23230000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ7344-4-4-444-4-200002-22-2-222000000−2i22i22i2−2i2000−232323−230000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ7444-4-4-444-4-200002-22-2-2220000002i2−2i2−2i22i200023−23−23230000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ7544-4-4-444-4-200002-22-2-2220000002i2−2i2−2i22i2000−232323−230000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ764-444-44-4-4-244-4-422-2-22-224-44-40000002-220000-2000000000-22-22000000000000000000000000000000000000000
χ774-444-44-4-4-244-4-422-2-22-22-44-440000002-220000-20000000002-22-2000000000000000000000000000000000000000
χ784-444-44-4-4-2-4-44422-2-22-220000000000-22-20000200000004i−4i00000000−2i−2i2i2i0000000000000000000000000000000
χ794-444-44-4-4-2-4-44422-2-22-220000000000-22-2000020000000−4i4i000000002i2i−2i−2i0000000000000000000000000000000
χ804-44-4-4-44444-44-4-4-4-4-4444000000000044-40000-40000000000000000000000000000000000000000000000000000
χ814-44-4-4-444-24-44-42222-2-2-20000000000-2-22−2i3−2i32i32i320000000000000002i3−2i300000000000000000000000000000000000
χ824-44-4-4-444-24-44-42222-2-2-20000000000-2-222i32i3−2i3−2i32000000000000000−2i32i300000000000000000000000000000000000
χ834-4-444-44-4-20000-22-22-22200004i−4i−2i22i2−2i22i2000−2i2i−2i2i0000000000000022−22000000i2−i2i2−i2−22−2200000000000000000000000
χ844-4-444-44-4-20000-22-22-22200004i−4i2i2−2i22i2−2i2000−2i2i−2i2i00000000000000−2222000000−i2i2−i2i22−22−200000000000000000000000
χ854-4-444-44-4-20000-22-22-2220000−4i4i−2i22i2−2i22i20002i−2i2i−2i00000000000000−2222000000i2−i2i2−i22−22−200000000000000000000000
χ864-4-444-44-4-20000-22-22-2220000−4i4i2i2−2i22i2−2i20002i−2i2i−2i0000000000000022−22000000−i2i2−i2i2−22−2200000000000000000000000
χ874-4-4-444-44400004-4-44-4-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ884-4-4-444-44400004-4-44-4-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ8988-88-8-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000

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