Finite Group Databasebeta

← Group #10868031

Character table — Group #10868031

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-111-1-1-111-1-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-111-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1-11-1-1-1-111-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-20000000000-2-2000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-20000000000-2-200000000000022-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-220000000000220000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-222111111-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222222-1-1-1-11111111111-1-1-1-100000000-2-1-1110000000000
χ29222-2-2-2-222-22-22-2-222-22-2002i2i−2i−2i00002-200002-2000000000000000002i2i−2i−2i00000000000022-2-20000002i−2i0000000
χ30222-2-2-2-222-22-22-2-222-22-2002i2i−2i−2i00002-200002-2000000000000000002i2i−2i−2i000000000000-2-222000000−2i2i0000000
χ31222-2-2-2-222-22-22-2-222-22-200−2i−2i2i2i00002-200002-200000000000000000−2i−2i2i2i00000000000022-2-2000000−2i2i0000000
χ32222-2-2-2-222-22-22-2-222-22-200−2i−2i2i2i00002-200002-200000000000000000−2i−2i2i2i000000000000-2-2220000002i−2i0000000
χ332-22-2-222-2200002-2-2-222-22i−2i0000−i2−i2i2i2002i2i−2i−2i0022-2-2000002−20000000000−i2−i2i2i222−2−2002i−2i−i2i2−i2i20000000000002−20
χ342-22-2-222-2200002-2-2-222-22i−2i0000−i2−i2i2i2002i2i−2i−2i00-2-222000002−20000000000−i2−i2i2i222−2−200−2i2ii2−i2i2−i2000000000000−220
χ352-22-2-222-2200002-2-2-222-22i−2i0000i2i2−i2−i2002i2i−2i−2i0022-2-200000−220000000000i2i2−i2−i2−2−222002i−2ii2−i2i2−i2000000000000−220
χ362-22-2-222-2200002-2-2-222-22i−2i0000i2i2−i2−i2002i2i−2i−2i00-2-22200000−220000000000i2i2−i2−i2−2−22200−2i2i−i2i2−i2i20000000000002−20
χ372-22-2-222-2200002-2-2-222-2−2i2i0000−i2−i2i2i200−2i−2i2i2i0022-2-200000−220000000000−i2−i2i2i2−2−22200−2i2i−i2i2−i2i2000000000000−220
χ382-22-2-222-2200002-2-2-222-2−2i2i0000−i2−i2i2i200−2i−2i2i2i00-2-22200000−220000000000−i2−i2i2i2−2−222002i−2ii2−i2i2−i20000000000002−20
χ392-22-2-222-2200002-2-2-222-2−2i2i0000i2i2−i2−i200−2i−2i2i2i0022-2-2000002−20000000000i2i2−i2−i222−2−200−2i2ii2−i2i2−i20000000000002−20
χ402-22-2-222-2200002-2-2-222-2−2i2i0000i2i2−i2−i200−2i−2i2i2i00-2-222000002−20000000000i2i2−i2−i222−2−2002i−2i−i2i2−i2i2000000000000−220
χ412-2-22-22-2222-2-22-222-22-2-20000000000220000-2-22i−2i2i−2i0002-20022-2-2000000000000002i−2i000000000000002i−2i00000
χ422-2-22-22-2222-2-22-222-22-2-20000000000220000-2-22i−2i2i−2i000-2200-2-222000000000000002i−2i00000000000000−2i2i00000
χ432-2-22-22-2222-2-22-222-22-2-20000000000220000-2-2−2i2i−2i2i0002-20022-2-200000000000000−2i2i00000000000000−2i2i00000
χ442-2-22-22-2222-2-22-222-22-2-20000000000220000-2-2−2i2i−2i2i000-2200-2-22200000000000000−2i2i000000000000002i−2i00000
χ452-2-22-22-222-222-2-222-22-2-2002i−2i2i−2i0000-2-20000222i−2i2i−2i00000000000002i−2i2i−2i00000000−2i2i00000000000000002-2000
χ462-2-22-22-222-222-2-222-22-2-2002i−2i2i−2i0000-2-2000022−2i2i−2i2i00000000000002i−2i2i−2i000000002i−2i0000000000000000-22000
χ472-2-22-22-222-222-2-222-22-2-200−2i2i−2i2i0000-2-20000222i−2i2i−2i0000000000000−2i2i−2i2i00000000−2i2i0000000000000000-22000
χ482-2-22-22-222-222-2-222-22-2-200−2i2i−2i2i0000-2-2000022−2i2i−2i2i0000000000000−2i2i−2i2i000000002i−2i00000000000000002-2000
χ492-2-2-22-222222-2-22-22-2-2-22002-2-222i−2i2i−2i-2200002-2000002i−2i00000000002-2-222i−2i2i−2i00000000000002i−2i000000000000
χ502-2-2-22-222222-2-22-22-2-2-22002-2-22−2i2i−2i2i-2200002-200000−2i2i00000000002-2-22−2i2i−2i2i0000000000000−2i2i000000000000
χ512-2-2-22-222222-2-22-22-2-2-2200-222-22i−2i2i−2i-2200002-200000−2i2i0000000000-222-22i−2i2i−2i0000000000000−2i2i000000000000
χ522-2-2-22-222222-2-22-22-2-2-2200-222-2−2i2i−2i2i-2200002-2000002i−2i0000000000-222-2−2i2i−2i2i00000000000002i−2i000000000000
χ532-2-2-22-222-122-2-2-11-1111-1002-2-222i−2i2i−2i1-13−33−3-11000002i−2i00003−33−33−3-111-1−ii−ii−i3i3−i3i3000000000−ii−i3i30000000000
χ542-2-2-22-222-122-2-2-11-1111-1002-2-222i−2i2i−2i1-1−33−33-11000002i−2i0000−33−33−33-111-1−ii−iii3−i3i3−i3000000000−iii3−i30000000000
χ552-2-2-22-222-122-2-2-11-1111-1002-2-22−2i2i−2i2i1-13−33−3-1100000−2i2i00003−33−33−3-111-1i−ii−ii3−i3i3−i3000000000i−ii3−i30000000000
χ562-2-2-22-222-122-2-2-11-1111-1002-2-22−2i2i−2i2i1-1−33−33-1100000−2i2i0000−33−33−33-111-1i−ii−i−i3i3−i3i3000000000i−i−i3i30000000000
χ572-2-2-22-222-122-2-2-11-1111-100-222-22i−2i2i−2i1-13−33−3-1100000−2i2i0000−33−333−31-1-11−ii−ii−i3i3−i3i3000000000i−ii3−i30000000000
χ582-2-2-22-222-122-2-2-11-1111-100-222-22i−2i2i−2i1-1−33−33-1100000−2i2i00003−33−3−331-1-11−ii−iii3−i3i3−i3000000000i−i−i3i30000000000
χ592-2-2-22-222-122-2-2-11-1111-100-222-2−2i2i−2i2i1-13−33−3-11000002i−2i0000−33−333−31-1-11i−ii−ii3−i3i3−i3000000000−ii−i3i30000000000
χ602-2-2-22-222-122-2-2-11-1111-100-222-2−2i2i−2i2i1-1−33−33-11000002i−2i00003−33−3−331-1-11i−ii−i−i3i3−i3i3000000000−iii3−i30000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000000000-2-200000000000000000000000000000000000
χ63444-4-4-4-4444-44-4-4-444-44-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-44-422-2-22-2200000000002-200002-20000000000023−23−23230000000000000000000000000000000000000
χ65444-4-4-4-44-24-44-422-2-22-2200000000002-200002-200000000000−232323−230000000000000000000000000000000000000
χ66444-4-4-4-44-2-44-4422-2-22-22004i4i−4i−4i0000-220000-2200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ67444-4-4-4-44-2-44-4422-2-22-2200−4i−4i4i4i0000-220000-22000000000000000002i2i−2i−2i0000000000000000000000000000000
χ6844-44-4-44-44000044-44-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6944-44-4-44-44000044-44-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7044-44-4-44-4-20000-2-22-222200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ7144-44-4-44-4-20000-2-22-222200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ7244-44-4-44-4-20000-2-22-2222000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ7344-44-4-44-4-20000-2-22-2222000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ7444-4-444-4-440000-4-4-444-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ7544-4-444-4-440000-4-4-444-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ764-4444-4-4-440000-44-4-4-444000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ774-4444-4-4-440000-44-4-4-4440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ784-44-4-444-4-20000-2222-2-224i−4i0000−2i2−2i22i22i200−2i−2i2i2i0000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ794-44-4-444-4-20000-2222-2-224i−4i00002i22i2−2i2−2i200−2i−2i2i2i00000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ804-44-4-444-4-20000-2222-2-22−4i4i0000−2i2−2i22i22i2002i2i−2i−2i00000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ814-44-4-444-4-20000-2222-2-22−4i4i00002i22i2−2i2−2i2002i2i−2i−2i0000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ824-4-44-44-44-24-4-442-2-22-2220000000000-2-200002200000004-400-2-2220000000000000000000000000000000000000
χ834-4-44-44-44-24-4-442-2-22-2220000000000-2-20000220000000-440022-2-20000000000000000000000000000000000000
χ844-4-44-44-44-2-444-42-2-22-222004i−4i4i−4i0000220000-2-200000000000000000−2i2i−2i2i0000000000000000000000000000000
χ854-4-44-44-44-2-444-42-2-22-22200−4i4i−4i4i0000220000-2-2000000000000000002i−2i2i−2i0000000000000000000000000000000
χ864-4-4-44-4444-4-4444-44-4-4-4400000000004-40000-440000000000000000000000000000000000000000000000000000
χ874-4-4-44-444-2-4-444-22-2222-20000000000-2223−2323−232-2000000000000000−232300000000000000000000000000000000000
χ884-4-4-44-444-2-4-444-22-2222-20000000000-22−2323−23232-200000000000000023−2300000000000000000000000000000000000
χ8988-8-888-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8888-8-8-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000

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