Finite Group Databasebeta

← Group #10828802

Character table — Group #10828802

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212222224444668812121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-111-1-1-11111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111111-1-1111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111111-1-111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1111-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-20000-2-2000000000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-20000-2-200000000000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000022000000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22000022000000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-2-2-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2-1-12211111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-1-1-2-21111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-22211-2-21111-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-211221111-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-211-2-2-1-1-1-11111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-222221122-1-1-1-111111111-1-1-1-100000000-211-1-10000000000
χ2922-222-2-2-22-2-2222-2-222-2-2002i2i−2i−2i00002-200002-2000000000000000002i2i−2i−2i00000000000022-2-200000000002i−2i000
χ3022-222-2-2-22-2-2222-2-222-2-2002i2i−2i−2i00002-200002-2000000000000000002i2i−2i−2i000000000000-2-2220000000000−2i2i000
χ3122-222-2-2-22-2-2222-2-222-2-200−2i−2i2i2i00002-200002-200000000000000000−2i−2i2i2i00000000000022-2-20000000000−2i2i000
χ3222-222-2-2-22-2-2222-2-222-2-200−2i−2i2i2i00002-200002-200000000000000000−2i−2i2i2i000000000000-2-22200000000002i−2i000
χ332-22-22-22-22-22-22-2222-2-2-2002i−2i2i−2i22-2-2-2-200002200000002i−2i000000002i−2i2i−2i22-2-20000000000000002i−2i0000000000
χ342-22-22-22-22-22-22-2222-2-2-2002i−2i2i−2i-2-222-2-20000220000000−2i2i000000002i−2i2i−2i-2-222000000000000000−2i2i0000000000
χ352-22-22-22-22-22-22-2222-2-2-200−2i2i−2i2i22-2-2-2-20000220000000−2i2i00000000−2i2i−2i2i22-2-2000000000000000−2i2i0000000000
χ362-22-22-22-22-22-22-2222-2-2-200−2i2i−2i2i-2-222-2-200002200000002i−2i00000000−2i2i−2i2i-2-2220000000000000002i−2i0000000000
χ372-22-22-22-2-1-22-221-1-1-1111002i−2i2i−2i22-2-211−i3−i3i3i3-1-100000002i−2i−i3i30033−3−3−ii−ii-1-111−i3−i3i3i30000000003−3−ii0000000000
χ382-22-22-22-2-1-22-221-1-1-1111002i−2i2i−2i22-2-211i3i3−i3−i3-1-100000002i−2ii3−i300−3−333−ii−ii-1-111i3i3−i3−i3000000000−33−ii0000000000
χ392-22-22-22-2-1-22-221-1-1-1111002i−2i2i−2i-2-22211−i3−i3i3i3-1-10000000−2i2i−i3i30033−3−3−ii−ii11-1-1i3i3−i3−i3000000000−33i−i0000000000
χ402-22-22-22-2-1-22-221-1-1-1111002i−2i2i−2i-2-22211i3i3−i3−i3-1-10000000−2i2ii3−i300−3−333−ii−ii11-1-1−i3−i3i3i30000000003−3i−i0000000000
χ412-22-22-22-2-1-22-221-1-1-111100−2i2i−2i2i22-2-211−i3−i3i3i3-1-10000000−2i2i−i3i300−3−333i−ii−i-1-111−i3−i3i3i3000000000−33i−i0000000000
χ422-22-22-22-2-1-22-221-1-1-111100−2i2i−2i2i22-2-211i3i3−i3−i3-1-10000000−2i2ii3−i30033−3−3i−ii−i-1-111i3i3−i3−i30000000003−3i−i0000000000
χ432-22-22-22-2-1-22-221-1-1-111100−2i2i−2i2i-2-22211−i3−i3i3i3-1-100000002i−2i−i3i300−3−333i−ii−i11-1-1i3i3−i3−i30000000003−3−ii0000000000
χ442-22-22-22-2-1-22-221-1-1-111100−2i2i−2i2i-2-22211i3i3−i3−i3-1-100000002i−2ii3−i30033−3−3i−ii−i11-1-1−i3−i3i3i3000000000−33−ii0000000000
χ452-2-22-222-220000-22-2-222-22i−2i00002−22−2002i−2i2i−2i0022-2-20000000−i2i2000000002−22−2−i2i2−i2i2002i−2i2−22−2000000000000−i2i20
χ462-2-22-222-220000-22-2-222-22i−2i00002−22−2002i−2i2i−2i00-2-2220000000−i2i2000000002−22−2−i2i2−i2i200−2i2i−22−22000000000000i2−i20
χ472-2-22-222-220000-22-2-222-22i−2i0000−22−22002i−2i2i−2i0022-2-20000000i2−i200000000−22−22i2−i2i2−i2002i−2i−22−22000000000000i2−i20
χ482-2-22-222-220000-22-2-222-22i−2i0000−22−22002i−2i2i−2i00-2-2220000000i2−i200000000−22−22i2−i2i2−i200−2i2i2−22−2000000000000−i2i20
χ492-2-22-222-220000-22-2-222-2−2i2i00002−22−200−2i2i−2i2i0022-2-20000000i2−i2000000002−22−2i2−i2i2−i200−2i2i2−22−2000000000000i2−i20
χ502-2-22-222-220000-22-2-222-2−2i2i00002−22−200−2i2i−2i2i00-2-2220000000i2−i2000000002−22−2i2−i2i2−i2002i−2i−22−22000000000000−i2i20
χ512-2-22-222-220000-22-2-222-2−2i2i0000−22−2200−2i2i−2i2i0022-2-20000000−i2i200000000−22−22−i2i2−i2i200−2i2i−22−22000000000000−i2i20
χ522-2-22-222-220000-22-2-222-2−2i2i0000−22−2200−2i2i−2i2i00-2-2220000000−i2i200000000−22−22−i2i2−i2i2002i−2i2−22−2000000000000i2−i20
χ532-2-2-222-2222-2-22-2-2-22-222002-2-220000-2200002-22-22-200000000000002-2-22000000002-2000000000000002-200000
χ542-2-2-222-2222-2-22-2-2-22-222002-2-220000-2200002-2-22-2200000000000002-2-2200000000-2200000000000000-2200000
χ552-2-2-222-2222-2-22-2-2-22-22200-222-20000-2200002-22-22-20000000000000-222-2000000002-200000000000000-2200000
χ562-2-2-222-2222-2-22-2-2-22-22200-222-20000-2200002-2-22-220000000000000-222-200000000-22000000000000002-200000
χ572-2-2-222-222-222-2-2-2-22-22200000000002-20000-222-22-202-20000002-22-2000000000000-22000000000002-200000000
χ582-2-2-222-222-222-2-2-2-22-22200000000002-20000-222-22-20-22000000-22-22000000000000-2200000000000-2200000000
χ592-2-2-222-222-222-2-2-2-22-22200000000002-20000-22-22-2202-20000002-22-20000000000002-200000000000-2200000000
χ602-2-2-222-222-222-2-2-2-22-22200000000002-20000-22-22-220-22000000-22-220000000000002-2000000000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400002200000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000-2-200000000000000000000000000000000000000000
χ63444-4-44-4-4400004-44-4-44-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-4-44-4-4400004-44-4-44-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-444-4-4-4444-4-44-4-444-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-244-4-4-222-2-22200000000002-200002-2000000000000023−23−232300000000000000000000000000000000000
χ6744-444-4-4-4-244-4-4-222-2-22200000000002-200002-20000000000000−232323−2300000000000000000000000000000000000
χ6844-444-4-4-4-2-4-444-222-2-222004i4i−4i−4i0000-220000-2200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6944-444-4-4-4-2-4-444-222-2-22200−4i−4i4i4i0000-220000-22000000000000000002i2i−2i−2i0000000000000000000000000000000
χ7044-4-4-4-4444000044-4-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7144-4-4-4-4444000044-4-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7244-4-4-4-444-20000-2-22222-200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ7344-4-4-4-444-20000-2-22222-200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ7444-4-4-4-444-20000-2-22222-2000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7544-4-4-4-444-20000-2-22222-2000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ764-444-4-4-4440000-4-44-44-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ774-444-4-4-4440000-4-44-44-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ784-44-44-44-444-44-4-4444-4-4-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ794-44-44-44-4-24-44-42-2-2-22220000000000-2-2−2i3−2i32i32i3220000000002i3−2i300000000000000000000000000000000000000000
χ804-44-44-44-4-24-44-42-2-2-22220000000000-2-22i32i3−2i3−2i322000000000−2i32i300000000000000000000000000000000000000000
χ814-4-44-444-4-200002-222-2-224i−4i000022−2222−2200−2i2i−2i2i0000000000000−2i22i200000000−22−22i2−i2i2−i200000000000000000000000
χ824-4-44-444-4-200002-222-2-224i−4i0000−2222−222200−2i2i−2i2i00000000000002i2−2i2000000002−22−2−i2i2−i2i200000000000000000000000
χ834-4-44-444-4-200002-222-2-22−4i4i000022−2222−22002i−2i2i−2i00000000000002i2−2i200000000−22−22−i2i2−i2i200000000000000000000000
χ844-4-44-444-4-200002-222-2-22−4i4i0000−2222−2222002i−2i2i−2i0000000000000−2i22i2000000002−22−2i2−i2i2−i200000000000000000000000
χ854-4-4-444-44-24-4-44222-22-2-2004-4-4400002-20000-2200000000000000000-222-20000000000000000000000000000000
χ864-4-4-444-44-24-4-44222-22-2-200-444-400002-20000-22000000000000000002-2-220000000000000000000000000000000
χ874-4-4-444-44-2-444-4222-22-2-20000000000-2200002-2000004-4000000-22-2200000000000000000000000000000000000
χ884-4-4-444-44-2-444-4222-22-2-20000000000-2200002-200000-440000002-22-200000000000000000000000000000000000
χ89888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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