Finite Group Databasebeta

← Group #10853380

Character table — Group #10853380

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-111-1-111-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-111-1-1111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111111-1-111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-111-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-2000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-200000000000022-2-20000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000020000002200000000000022220000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-222-2-2-2-1-1-1-1111111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-2-2-22221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ2922-22-22-2-2222-2-22-22-22-2-222-2-2000000220000-2-222-2-2000000022-2-2000000000000002-200000000000002-2000000
χ3022-22-22-2-2222-2-22-22-22-2-222-2-2000000220000-2-2-2-222000000022-2-200000000000000-220000000000000-22000000
χ3122-22-22-2-2222-2-22-22-22-2-2-2-222000000220000-2-222-2-20000000-2-222000000000000002-20000000000000-22000000
χ3222-22-22-2-2222-2-22-22-22-2-2-2-222000000220000-2-2-2-2220000000-2-22200000000000000-2200000000000002-2000000
χ3322-22-22-2-22-2-2222-22-22-2-20000000000-2-200002222-2-22i−2i000000000002i2i−2i−2i00000000-22000000000002i−2i00000000
χ3422-22-22-2-22-2-2222-22-22-2-20000000000-2-200002222-2-2−2i2i00000000000−2i−2i2i2i00000000-2200000000000−2i2i00000000
χ3522-22-22-2-22-2-2222-22-22-2-20000000000-2-2000022-2-2222i−2i000000000002i2i−2i−2i000000002-200000000000−2i2i00000000
χ3622-22-22-2-22-2-2222-22-22-2-20000000000-2-2000022-2-222−2i2i00000000000−2i−2i2i2i000000002-2000000000002i−2i00000000
χ372-22-222-2-222-2-22-222-2-2-222i−2i2i−2i002i2i−2i−2i2-200002-20000002-20002i−2i2i−2i0000002i2i−2i−2i0000000000000002-20000000000
χ382-22-222-2-222-2-22-222-2-2-222i−2i2i−2i00−2i−2i2i2i2-200002-2000000-220002i−2i2i−2i000000−2i−2i2i2i000000000000000-220000000000
χ392-22-222-2-222-2-22-222-2-2-22−2i2i−2i2i002i2i−2i−2i2-200002-2000000-22000−2i2i−2i2i0000002i2i−2i−2i000000000000000-220000000000
χ402-22-222-2-222-2-22-222-2-2-22−2i2i−2i2i00−2i−2i2i2i2-200002-20000002-2000−2i2i−2i2i000000−2i−2i2i2i0000000000000002-20000000000
χ412-22-222-2-2-12-2-221-1-1111-12i−2i2i−2i002i2i−2i−2i-1133−3−3-110000002-2000−ii−ii3−3−i3i3−i3i3−i−iii−i3−i3i3i30000000003−3-110000000000
χ422-22-222-2-2-12-2-221-1-1111-12i−2i2i−2i002i2i−2i−2i-11−3−333-110000002-2000−ii−ii−33i3−i3i3−i3−i−iiii3i3−i3−i3000000000−33-110000000000
χ432-22-222-2-2-12-2-221-1-1111-12i−2i2i−2i00−2i−2i2i2i-1133−3−3-11000000-22000−ii−ii3−3−i3i3−i3i3ii−i−ii3i3−i3−i3000000000−331-10000000000
χ442-22-222-2-2-12-2-221-1-1111-12i−2i2i−2i00−2i−2i2i2i-11−3−333-11000000-22000−ii−ii−33i3−i3i3−i3ii−i−i−i3−i3i3i30000000003−31-10000000000
χ452-22-222-2-2-12-2-221-1-1111-1−2i2i−2i2i002i2i−2i−2i-1133−3−3-11000000-22000i−ii−i3−3i3−i3i3−i3−i−iii−i3−i3i3i3000000000−331-10000000000
χ462-22-222-2-2-12-2-221-1-1111-1−2i2i−2i2i002i2i−2i−2i-11−3−333-11000000-22000i−ii−i−33−i3i3−i3i3−i−iiii3i3−i3−i30000000003−31-10000000000
χ472-22-222-2-2-12-2-221-1-1111-1−2i2i−2i2i00−2i−2i2i2i-1133−3−3-110000002-2000i−ii−i3−3i3−i3i3−i3ii−i−ii3i3−i3−i30000000003−3-110000000000
χ482-22-222-2-2-12-2-221-1-1111-1−2i2i−2i2i00−2i−2i2i2i-11−3−333-110000002-2000i−ii−i−33−i3i3−i3i3ii−i−i−i3−i3i3i3000000000−33-110000000000
χ492-2-222-2-2220000-22-2-222-200002i−2i−i2i2−i2i2002i−2i2i−2i002i−2i2i−2i000002−20000000000−i2i2−i2i22−22−2002-222−2−2000000000000−i2i20
χ502-2-222-2-2220000-22-2-222-200002i−2i−i2i2−i2i2002i−2i2i−2i00−2i2i−2i2i000002−20000000000−i2i2−i2i22−22−200-22−2−222000000000000i2−i20
χ512-2-222-2-2220000-22-2-222-200002i−2ii2−i2i2−i2002i−2i2i−2i002i−2i2i−2i00000−220000000000i2−i2i2−i2−22−22002-2−2−222000000000000i2−i20
χ522-2-222-2-2220000-22-2-222-200002i−2ii2−i2i2−i2002i−2i2i−2i00−2i2i−2i2i00000−220000000000i2−i2i2−i2−22−2200-2222−2−2000000000000−i2i20
χ532-2-222-2-2220000-22-2-222-20000−2i2i−i2i2−i2i200−2i2i−2i2i002i−2i2i−2i00000−220000000000−i2i2−i2i2−22−2200-2222−2−2000000000000i2−i20
χ542-2-222-2-2220000-22-2-222-20000−2i2i−i2i2−i2i200−2i2i−2i2i00−2i2i−2i2i00000−220000000000−i2i2−i2i2−22−22002-2−2−222000000000000−i2i20
χ552-2-222-2-2220000-22-2-222-20000−2i2ii2−i2i2−i200−2i2i−2i2i002i−2i2i−2i000002−20000000000i2−i2i2−i22−22−200-22−2−222000000000000−i2i20
χ562-2-222-2-2220000-22-2-222-20000−2i2ii2−i2i2−i200−2i2i−2i2i00−2i2i−2i2i000002−20000000000i2−i2i2−i22−22−2002-222−2−2000000000000i2−i20
χ572-2-2-2-222222-22-2-2-222-22-22i−2i−2i2i0000002-20000-22000000000002i−2i−2i2i0000000000000000002i−2i2i−2i00000000002-2000
χ582-2-2-2-222222-22-2-2-222-22-22i−2i−2i2i0000002-20000-22000000000002i−2i−2i2i000000000000000000−2i2i−2i2i0000000000-22000
χ592-2-2-2-222222-22-2-2-222-22-2−2i2i2i−2i0000002-20000-2200000000000−2i2i2i−2i0000000000000000002i−2i2i−2i0000000000-22000
χ602-2-2-2-222222-22-2-2-222-22-2−2i2i2i−2i0000002-20000-2200000000000−2i2i2i−2i000000000000000000−2i2i−2i2i00000000002-2000
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
χ63444-4-4-4-44400004-4-4-4-444000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ64444-4-4-4-44400004-4-4-4-4440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ6544-44-44-4-4-244-4-4-22-22-22244-4-4000000-2-200002200000000000-2-2220000000000000000000000000000000000000
χ6644-44-44-4-4-244-4-4-22-22-222-4-444000000-2-20000220000000000022-2-20000000000000000000000000000000000000
χ6744-44-44-4-4-2-4-444-22-22-2220000000000220000-2-200004i−4i00000000000−2i−2i2i2i0000000000000000000000000000000
χ6844-44-44-4-4-2-4-444-22-22-2220000000000220000-2-20000−4i4i000000000002i2i−2i−2i0000000000000000000000000000000
χ6944-4-44-44-44000044-44-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7044-4-44-44-44000044-44-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7144-4-44-44-4-20000-2-22-222200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ7244-4-44-44-4-20000-2-22-222200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ7344-4-44-44-4-20000-2-22-2222000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ7444-4-44-44-4-20000-2-22-2222000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ754-444-4-44-440000-4-4-444-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ764-444-4-44-440000-4-4-444-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ774-44-444-4-44-444-4-444-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ784-44-444-4-4-2-444-42-2-2222-200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ794-44-444-4-4-2-444-42-2-2222-200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ804-4-444-4-44-200002-222-2-2200004i−4i−2i22i2−2i22i200−2i2i−2i2i0000000000022−220000000000i2−i2i2−i2−22−2200000000000000000000000
χ814-4-444-4-44-200002-222-2-2200004i−4i2i2−2i22i2−2i200−2i2i−2i2i00000000000−22220000000000−i2i2−i2i22−22−200000000000000000000000
χ824-4-444-4-44-200002-222-2-220000−4i4i−2i22i2−2i22i2002i−2i2i−2i00000000000−22220000000000i2−i2i2−i22−22−200000000000000000000000
χ834-4-444-4-44-200002-222-2-220000−4i4i2i2−2i22i2−2i2002i−2i2i−2i0000000000022−220000000000−i2i2−i2i2−22−2200000000000000000000000
χ844-4-4-4-44444-44-44-4-444-44-40000000000-4400004-40000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-24-44-422-2-22-224i−4i−4i4i000000-2200002-200000000000−2i2i2i−2i0000000000000000000000000000000000000
χ864-4-4-4-4444-24-44-422-2-22-22−4i4i4i−4i000000-2200002-2000000000002i−2i−2i2i0000000000000000000000000000000000000
χ874-4-4-4-4444-2-44-4422-2-22-2200000000002-20000-220000000000000000023−23−23230000000000000000000000000000000
χ884-4-4-4-4444-2-44-4422-2-22-2200000000002-20000-2200000000000000000−232323−230000000000000000000000000000000
χ89888-8-8-8-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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