Finite Group Databasebeta

← Group #10827336

Character table — Group #10827336

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121222222222466668812121212121224242424242424242244888846612122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-111-1-111-111-1-1-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11-1-111-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111111-1-111111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-200000000000022-2-200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-2000000000000-2-2220000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000200000022000000000000222200000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-222-21111-2-211-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-211112211-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-2-2-22111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-2-1-1-1-1221111111111-1-1-1-100000000-2-1-1110000000000
χ2922-2-22-22-222-22-22-2-22-22-22i2i−2i−2i000000220000-2-2000000000000000002i2i−2i−2i0000000000002i2i−2i−2i000002-200000000
χ3022-2-22-22-222-22-22-2-22-22-22i2i−2i−2i000000220000-2-2000000000000000002i2i−2i−2i000000000000−2i−2i2i2i00000-2200000000
χ3122-2-22-22-222-22-22-2-22-22-2−2i−2i2i2i000000220000-2-200000000000000000−2i−2i2i2i0000000000002i2i−2i−2i00000-2200000000
χ3222-2-22-22-222-22-22-2-22-22-2−2i−2i2i2i000000220000-2-200000000000000000−2i−2i2i2i000000000000−2i−2i2i2i000002-200000000
χ332-22-2-222-2222-2-2-2222-2-2-22i−2i2i−2i002i2i−2i−2i2-200002-20000002-20000000002i−2i2i−2i2i2i−2i−2i00000000000002-2000000000000
χ342-22-2-222-2222-2-2-2222-2-2-22i−2i2i−2i00−2i−2i2i2i2-200002-2000000-220000000002i−2i2i−2i−2i−2i2i2i0000000000000-22000000000000
χ352-22-2-222-2222-2-2-2222-2-2-2−2i2i−2i2i002i2i−2i−2i2-200002-2000000-22000000000−2i2i−2i2i2i2i−2i−2i0000000000000-22000000000000
χ362-22-2-222-2222-2-2-2222-2-2-2−2i2i−2i2i00−2i−2i2i2i2-200002-20000002-2000000000−2i2i−2i2i−2i−2i2i2i00000000000002-2000000000000
χ372-22-2-222-2-122-2-21-1-1-11112i−2i2i−2i002i2i−2i−2i-1133−3−3-110000002-20−i3−i3i3i3003−3−ii−ii−i−iii−i3−i3i3i3000000000-113−30000000000
χ382-22-2-222-2-122-2-21-1-1-11112i−2i2i−2i002i2i−2i−2i-11−3−333-110000002-20i3i3−i3−i300−33−ii−ii−i−iiii3i3−i3−i3000000000-11−330000000000
χ392-22-2-222-2-122-2-21-1-1-11112i−2i2i−2i00−2i−2i2i2i-1133−3−3-11000000-220−i3−i3i3i3003−3−ii−iiii−i−ii3i3−i3−i30000000001-1−330000000000
χ402-22-2-222-2-122-2-21-1-1-11112i−2i2i−2i00−2i−2i2i2i-11−3−333-11000000-220i3i3−i3−i300−33−ii−iiii−i−i−i3−i3i3i30000000001-13−30000000000
χ412-22-2-222-2-122-2-21-1-1-1111−2i2i−2i2i002i2i−2i−2i-1133−3−3-11000000-220i3i3−i3−i3003−3i−ii−i−i−iii−i3−i3i3i30000000001-1−330000000000
χ422-22-2-222-2-122-2-21-1-1-1111−2i2i−2i2i002i2i−2i−2i-11−3−333-11000000-220−i3−i3i3i300−33i−ii−i−i−iiii3i3−i3−i30000000001-13−30000000000
χ432-22-2-222-2-122-2-21-1-1-1111−2i2i−2i2i00−2i−2i2i2i-1133−3−3-110000002-20i3i3−i3−i3003−3i−ii−iii−i−ii3i3−i3−i3000000000-113−30000000000
χ442-22-2-222-2-122-2-21-1-1-1111−2i2i−2i2i00−2i−2i2i2i-11−3−333-110000002-20−i3−i3i3i300−33i−ii−iii−i−i−i3−i3i3i3000000000-11−330000000000
χ452-2-22-2-22222-2-22-2-2-222-222-2-220000002-20000-2222-2-200000000000002-2-2200000000002-20000000000002-200000
χ462-2-22-2-22222-2-22-2-2-222-222-2-220000002-20000-22-2-22200000000000002-2-220000000000-22000000000000-2200000
χ472-2-22-2-22222-2-22-2-2-222-22-222-20000002-20000-2222-2-20000000000000-222-200000000002-2000000000000-2200000
χ482-2-22-2-22222-2-22-2-2-222-22-222-20000002-20000-22-2-2220000000000000-222-20000000000-220000000000002-200000
χ492-2-22-2-2222-222-2-2-2-222-220000000000-2200002-222-2-22-20002-22-2000000000000000000-22000000000000002-2000
χ502-2-22-2-2222-222-2-2-2-222-220000000000-2200002-222-2-2-22000-22-22000000000000000000-2200000000000000-22000
χ512-2-22-2-2222-222-2-2-2-222-220000000000-2200002-2-2-2222-20002-22-20000000000000000002-200000000000000-22000
χ522-2-22-2-2222-222-2-2-2-222-220000000000-2200002-2-2-222-22000-22-220000000000000000002-2000000000000002-2000
χ532-2-2-222-2220000-22-2-2-22200002-22−22−2002-22-2002-22-20000000002−20000002−22−22−22−22-2002−22−20000000000002−20
χ542-2-2-222-2220000-22-2-2-22200002-22−22−2002-22-200-22-220000000002−20000002−22−22−22−2-2200−22−22000000000000−220
χ552-2-2-222-2220000-22-2-2-22200002-2−22−22002-22-2002-22-2000000000−22000000−22−22−22−222-200−22−22000000000000−220
χ562-2-2-222-2220000-22-2-2-22200002-2−22−22002-22-200-22-22000000000−22000000−22−22−22−22-22002−22−20000000000002−20
χ572-2-2-222-2220000-22-2-2-2220000-222−22−200-22-22002-22-2000000000−220000002−22−2−22−22-22002−22−2000000000000−220
χ582-2-2-222-2220000-22-2-2-2220000-222−22−200-22-2200-22-22000000000−220000002−22−2−22−222-200−22−220000000000002−20
χ592-2-2-222-2220000-22-2-2-2220000-22−22−2200-22-22002-22-20000000002−2000000−22−222−22−2-2200−22−220000000000002−20
χ602-2-2-222-2220000-22-2-2-2220000-22−22−2200-22-2200-22-220000000002−2000000−22−222−22−22-2002−22−2000000000000−220
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-22200000000-40000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000004000000-2-200000000000000000000000000000000000
χ63444-4-4-4-44400004-44-4-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-4-4-4-44400004-44-4-4-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-44-44-4-44000044-4-44-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ6644-44-44-4-44000044-4-44-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ6744-44-44-4-4-20000-2-222-222000000−2i22i22i2−2i20023−23−232300000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ6844-44-44-4-4-20000-2-222-222000000−2i22i22i2−2i200−232323−2300000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ6944-44-44-4-4-20000-2-222-2220000002i2−2i2−2i22i20023−23−232300000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ7044-44-44-4-4-20000-2-222-2220000002i2−2i2−2i22i200−232323−2300000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ7144-4-44-44-44-44-444-4-44-44-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ7244-4-44-44-4-24-44-4-222-22-224i4i−4i−4i000000-2-200002200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ7344-4-44-44-4-24-44-4-222-22-22−4i−4i4i4i000000-2-2000022000000000000000002i2i−2i−2i0000000000000000000000000000000
χ7444-4-44-44-4-2-44-44-222-22-220000000000220000-2-2000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ7544-4-44-44-4-2-44-44-222-22-220000000000220000-2-20000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ764-4444-4-4-440000-4-44-444-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ774-4444-4-4-440000-4-44-444-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ784-44-4-444-44-4-444-4444-4-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ794-44-4-444-4-2-4-4442-2-2-222200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ804-44-4-444-4-2-4-4442-2-2-222200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ814-4-44-4-444-24-4-44222-2-22-24-4-44000000-2200002-200000000000000000-222-20000000000000000000000000000000
χ824-4-44-4-444-24-4-44222-2-22-2-444-4000000-2200002-2000000000000000002-2-220000000000000000000000000000000
χ834-4-44-4-444-2-444-4222-2-22-200000000002-20000-2200004-4000-22-22000000000000000000000000000000000000000
χ844-4-44-4-444-2-444-4222-2-22-200000000002-20000-220000-440002-22-2000000000000000000000000000000000000000
χ854-4-4-444-44-200002-2222-2-200004-422−2222−2200-22-2200000000000000022−22000000−22−22−22−2200000000000000000000000
χ864-4-4-444-44-200002-2222-2-200004-4−2222−222200-22-22000000000000000−22220000002−22−22−22−200000000000000000000000
χ874-4-4-444-44-200002-2222-2-20000-4422−2222−22002-22-2000000000000000−2222000000−22−222−22−200000000000000000000000
χ884-4-4-444-44-200002-2222-2-20000-44−2222−2222002-22-200000000000000022−220000002−22−2−22−2200000000000000000000000
χ89888-8-8-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8888-8-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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