Finite Group Databasebeta

← Group #10853305

Character table — Group #10853305

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ9111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-11-11-1
χ10111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-11-11
χ11111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1-11
χ12111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-111-1
χ13111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-11-11
χ14111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111111-11-1
χ15111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-111-1
χ16111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111-1-11
χ172222222222222-2-2-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000222200000000000000-2-200
χ182222222222222-2-2-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000-2-2-2-2000000000000002200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000022-2-200000000000000-2200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000-2-222000000000000002-200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-10000000000000000-1-111000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000000011-1-1000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222-2-22222-2-211-1-1-1-11111-1-1-1-11111000000000000000011-1-1000000
χ2922-222-2-2-2200002-2-222-22-2-2-22002-2-20000200002-200000000000022-2-2000000002i2i−2i−2i00002i2i−2i−2i00000000000000
χ3022-222-2-2-2200002-2-222-22-2-2-22002-2-20000200002-200000000000022-2-200000000−2i−2i2i2i0000−2i−2i2i2i00000000000000
χ3122-222-2-2-2200002-2-222-22-2-2-22002-2-2000020000-22000000000000-2-222000000002i2i−2i−2i0000−2i−2i2i2i00000000000000
χ3222-222-2-2-2200002-2-222-22-2-2-22002-2-2000020000-22000000000000-2-22200000000−2i−2i2i2i00002i2i−2i−2i00000000000000
χ332-222-2-22-2222-2-20000-2-2-22-2220000022-2-20000000002−22−2000000000022−2−222−2−200002i−2i2i−2i−i2i2−i2i2−i2−i2i2i20000000000
χ342-222-2-22-2222-2-20000-2-2-22-2220000022-2-20000000002−22−2000000000022−2−222−2−20000−2i2i−2i2ii2−i2i2−i2i2i2−i2−i20000000000
χ352-222-2-22-2222-2-20000-2-2-22-2220000022-2-2000000000−22−220000000000−2−222−2−22200002i−2i2i−2ii2−i2i2−i2i2i2−i2−i20000000000
χ362-222-2-22-2222-2-20000-2-2-22-2220000022-2-2000000000−22−220000000000−2−222−2−2220000−2i2i−2i2i−i2i2−i2i2−i2−i2i2i20000000000
χ372-222-2-22-22-2-2220000-2-2-22-22200000-2-2220000000002−2−22000000000022−2−2−2−22200002i−2i−2i2i−i2i2−i2i2i2i2−i2−i20000000000
χ382-222-2-22-22-2-2220000-2-2-22-22200000-2-2220000000002−2−22000000000022−2−2−2−2220000−2i2i2i−2ii2−i2i2−i2−i2−i2i2i20000000000
χ392-222-2-22-22-2-2220000-2-2-22-22200000-2-222000000000−222−20000000000−2−22222−2−200002i−2i−2i2ii2−i2i2−i2−i2−i2i2i20000000000
χ402-222-2-22-22-2-2220000-2-2-22-22200000-2-222000000000−222−20000000000−2−22222−2−20000−2i2i2i−2i−i2i2−i2i2i2i2−i2−i20000000000
χ412-22-222-2-222-22-222-2-2-2-2222-2-22-222-22-22-2-20000000000002-200000000000000002-22-200000000000000002-20000
χ422-22-222-2-222-22-222-2-2-2-2222-2-22-222-22-22-2-20000000000002-20000000000000000-22-220000000000000000-220000
χ432-22-222-2-222-22-2-2-222-2-2222-2-2-22-2-222-22-222i−2i2i−2i00000000-22000000000000000000000000000000002i−2i2i−2i000000
χ442-22-222-2-222-22-2-2-222-2-2222-2-2-22-2-222-22-22−2i2i−2i2i00000000-2200000000000000000000000000000000−2i2i−2i2i000000
χ452-22-222-2-22-22-2222-2-2-2-2222-2-2-2222-2-22-22-2000000000000-2200000000000000002-22-20000000000000000-220000
χ462-22-222-2-22-22-2222-2-2-2-2222-2-2-2222-2-22-22-2000000000000-220000000000000000-22-2200000000000000002-20000
χ472-22-222-2-22-22-22-2-222-2-2222-2-22-2-2-22-22-2222i−2i−2i2i000000002-2000000000000000000000000000000002i−2i−2i2i000000
χ482-22-222-2-22-22-22-2-222-2-2222-2-22-2-2-22-22-222−2i2i2i−2i000000002-200000000000000000000000000000000−2i2i2i−2i000000
χ492-22-222-2-2-12-22-2-2-22211-1-1-111-2211-1-11-11-12i−2i2i−2i000000001-133−3−33−33−3−i3i3−i3i3−i3i3−i3i30000000000000000−ii−ii000000
χ502-22-222-2-2-12-22-2-2-22211-1-1-111-2211-1-11-11-12i−2i2i−2i000000001-1−3−333−33−33i3−i3i3−i3i3−i3i3−i30000000000000000−ii−ii000000
χ512-22-222-2-2-12-22-2-2-22211-1-1-111-2211-1-11-11-1−2i2i−2i2i000000001-133−3−33−33−3i3−i3i3−i3i3−i3i3−i30000000000000000i−ii−i000000
χ522-22-222-2-2-12-22-2-2-22211-1-1-111-2211-1-11-11-1−2i2i−2i2i000000001-1−3−333−33−33−i3i3−i3i3−i3i3−i3i30000000000000000i−ii−i000000
χ532-22-222-2-2-1-22-22-2-22211-1-1-1112-211-11-11-1-12i−2i−2i2i00000000-1133−3−3−33−33i3−i3i3−i3−i3i3−i3i30000000000000000−iii−i000000
χ542-22-222-2-2-1-22-22-2-22211-1-1-1112-211-11-11-1-12i−2i−2i2i00000000-11−3−3333−33−3−i3i3−i3i3i3−i3i3−i30000000000000000−iii−i000000
χ552-22-222-2-2-1-22-22-2-22211-1-1-1112-211-11-11-1-1−2i2i2i−2i00000000-1133−3−3−33−33−i3i3−i3i3i3−i3i3−i30000000000000000i−i−ii000000
χ562-22-222-2-2-1-22-22-2-22211-1-1-1112-211-11-11-1-1−2i2i2i−2i00000000-11−3−3333−33−3i3−i3i3−i3−i3i3−i3i30000000000000000i−i−ii000000
χ572-2-2-22-222200002-22-2-222-2-22-2002-220000-20000002-20000002-22-20000000000002i−2i−2i2i000000002i−2i2i−2i0000000000
χ582-2-2-22-222200002-22-2-222-2-22-2002-220000-20000002-20000002-22-2000000000000−2i2i2i−2i00000000−2i2i−2i2i0000000000
χ592-2-2-22-222200002-22-2-222-2-22-2002-220000-2000000-22000000-22-220000000000002i−2i−2i2i00000000−2i2i−2i2i0000000000
χ602-2-2-22-222200002-22-2-222-2-22-2002-220000-2000000-22000000-22-22000000000000−2i2i2i−2i000000002i−2i2i−2i0000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ63444-4-4-4-4444-4-44000044-44-4-4-4000004-4-44000000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-444-444-4000044-44-4-4-400000-444-4000000000000000000000000000000000000000000000000000000000
χ65444-4-4-4-44-24-4-440000-2-22-222200000-222-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ66444-4-4-4-44-24-4-440000-2-22-222200000-222-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ67444-4-4-4-44-2-444-40000-2-22-2222000002-2-2200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ68444-4-4-4-44-2-444-40000-2-22-2222000002-2-2200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6944-444-4-4-440000-444-44-44-4-4-4400-4440000-400000000000000000000000000000000000000000000000000000000
χ7044-444-4-4-4-200004-4-44-22-2222-200-2220000-200004-4000000000000-2-2220000000000000000000000000000000000
χ7144-444-4-4-4-200004-4-44-22-2222-200-2220000-20000-4400000000000022-2-20000000000000000000000000000000000
χ7244-444-4-4-4-20000-444-4-22-2222-2002-2-2000020000000000000023−23−232300000000000000000000000000000000000000
χ7344-444-4-4-4-20000-444-4-22-2222-2002-2-20000200000000000000−232323−2300000000000000000000000000000000000000
χ7444-4-4-444-44000000004-4-4-444-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ7544-4-4-444-44000000004-4-4-444-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ764-444-4-44-4-244-4-40000222-22-2-200000-2-22200000000022−2222−220000000000−2−222−2−22200000000000000000000000000
χ774-444-4-44-4-244-4-40000222-22-2-200000-2-222000000000−2222−2222000000000022−2−222−2−200000000000000000000000000
χ784-444-4-44-4-2-4-4440000222-22-2-20000022-2-200000000022−22−22220000000000−2−22222−2−200000000000000000000000000
χ794-444-4-44-4-2-4-4440000222-22-2-20000022-2-2000000000−222222−22000000000022−2−2−2−22200000000000000000000000000
χ804-44-444-4-4-24-44-444-4-422-2-2-2224-4-2-22-22-222000000000000-22000000000000000000000000000000000000000000
χ814-44-444-4-4-2-44-4444-4-422-2-2-222-44-2-222-22-220000000000002-2000000000000000000000000000000000000000000
χ824-4-44-44-44400000000-44-4-44-4400000000000000000000000000000000000000000000000022−22−222200000000000000
χ834-4-44-44-44400000000-44-4-44-44000000000000000000000000000000000000000000000000−222222−2200000000000000
χ844-4-4-44-44440000-44-44-444-4-44-400-44-40000400000000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-200004-44-42-2-222-2200-22-2000020000004-4000000-22-2200000000000000000000000000000000000000
χ864-4-4-44-444-200004-44-42-2-222-2200-22-200002000000-440000002-22-200000000000000000000000000000000000000
χ874-4-4-44-444-20000-44-442-2-222-22002-220000-200000000000000000023−23−23230000000000000000000000000000000000
χ884-4-4-44-444-20000-44-442-2-222-22002-220000-2000000000000000000−232323−230000000000000000000000000000000000
χ8988-8-8-888-8-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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