Finite Group Databasebeta

← Group #10858915

Character table — Group #10858915

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121222224444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-111111111111-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-1-11111-1-1-1
χ1011111111111111111111-1-111111111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-111-1-1-1-11-1-111-1-11
χ17222222222-2-2-2-222222222200000000-2-2-22222-2222200-2000000000000-2-200000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222222200000000-2-2-22222-2-2-2-2-200-2000000000000-2-20000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000000000002200000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20020000000000002200000000222200000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-22-2-22211111111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-211111111-1-111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-1-11111-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-11111-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-1000022-2-2-2-2-21111-1-1-1-111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-1000022-222221111-1-1-1-1111111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-2222-2-22-222-2-2-2000000000022-20000-222-2-22-200000000022-2-200000000002-2000000000002-200000000
χ30222-2-22-2-2222-2-22-222-2-2-2000000000022-20000-222-2-2-22000000000-2-22200000000002-200000000000-2200000000
χ31222-2-22-2-2222-2-22-222-2-2-2000000000022-20000-2-2-2222-200000000022-2-20000000000-2200000000000-2200000000
χ32222-2-22-2-2222-2-22-222-2-2-2000000000022-20000-2-2-222-22000000000-2-2220000000000-22000000000002-200000000
χ33222-2-22-2-22-2-2222-222-2-2-2002i2i−2i−2i0000-2-220000222-2-200000002i2i−2i−2i00000000000000-2200000000000000002i−2i000
χ34222-2-22-2-22-2-2222-222-2-2-2002i2i−2i−2i0000-2-2200002-2-22200000002i2i−2i−2i000000000000002-20000000000000000−2i2i000
χ35222-2-22-2-22-2-2222-222-2-2-200−2i−2i2i2i0000-2-220000222-2-20000000−2i−2i2i2i00000000000000-220000000000000000−2i2i000
χ36222-2-22-2-22-2-2222-222-2-2-200−2i−2i2i2i0000-2-2200002-2-2220000000−2i−2i2i2i000000000000002-200000000000000002i−2i000
χ372-222-2-22-220000-22-22-22-22i−2i0000−i2−i2i2i20002i2i−2i−2i02-22-2000002−20000000000−i2−i2i2i222−2−2002i−2i−i2−i2i2i20000000000002−20
χ382-222-2-22-220000-22-22-22-22i−2i0000−i2−i2i2i20002i2i−2i−2i0-22-22000002−20000000000−i2−i2i2i222−2−200−2i2ii2i2−i2−i2000000000000−220
χ392-222-2-22-220000-22-22-22-22i−2i0000i2i2−i2−i20002i2i−2i−2i02-22-200000−220000000000i2i2−i2−i2−2−222002i−2ii2i2−i2−i2000000000000−220
χ402-222-2-22-220000-22-22-22-22i−2i0000i2i2−i2−i20002i2i−2i−2i0-22-2200000−220000000000i2i2−i2−i2−2−22200−2i2i−i2−i2i2i20000000000002−20
χ412-222-2-22-220000-22-22-22-2−2i2i0000−i2−i2i2i2000−2i−2i2i2i02-22-200000−220000000000−i2−i2i2i2−2−22200−2i2i−i2−i2i2i2000000000000−220
χ422-222-2-22-220000-22-22-22-2−2i2i0000−i2−i2i2i2000−2i−2i2i2i0-22-2200000−220000000000−i2−i2i2i2−2−222002i−2ii2i2−i2−i20000000000002−20
χ432-222-2-22-220000-22-22-22-2−2i2i0000i2i2−i2−i2000−2i−2i2i2i02-22-2000002−20000000000i2i2−i2−i222−2−200−2i2ii2i2−i2−i20000000000002−20
χ442-222-2-22-220000-22-22-22-2−2i2i0000i2i2−i2−i2000−2i−2i2i2i0-22-22000002−20000000000i2i2−i2−i222−2−2002i−2i−i2−i2i2i2000000000000−220
χ452-2-22-22-2222-22-2-222-22-2-2002-22-200002-220000-2000000000002-22-20000000000000000002i−2i2i−2i000000002i−2i00000
χ462-2-22-22-2222-22-2-222-22-2-2002-22-200002-220000-2000000000002-22-2000000000000000000−2i2i−2i2i00000000−2i2i00000
χ472-2-22-22-2222-22-2-222-22-2-200-22-2200002-220000-200000000000-22-220000000000000000002i−2i2i−2i00000000−2i2i00000
χ482-2-22-22-2222-22-2-222-22-2-200-22-2200002-220000-200000000000-22-22000000000000000000−2i2i−2i2i000000002i−2i00000
χ492-2-2-2222-22-222-2-2-22-2-222002i−2i−2i2i2i−2i2i−2i-2220000-200000002-2002i−2i−2i2i0000002i−2i2i−2i00000000000002-2000000000000
χ502-2-2-2222-22-222-2-2-22-2-222002i−2i−2i2i−2i2i−2i2i-2220000-20000000-22002i−2i−2i2i000000−2i2i−2i2i0000000000000-22000000000000
χ512-2-2-2222-22-222-2-2-22-2-22200−2i2i2i−2i2i−2i2i−2i-2220000-20000000-2200−2i2i2i−2i0000002i−2i2i−2i0000000000000-22000000000000
χ522-2-2-2222-22-222-2-2-22-2-22200−2i2i2i−2i−2i2i−2i2i-2220000-200000002-200−2i2i2i−2i000000−2i2i−2i2i00000000000002-2000000000000
χ532-2-2-2222-2-1-222-211-111-1-1002i−2i−2i2i2i−2i2i−2i1-1-1−i3i3−i3i3100000002-200−iii−i3−33−3−i3i3−ii−ii3−33−3000000000-11−i3i30000000000
χ542-2-2-2222-2-1-222-211-111-1-1002i−2i−2i2i2i−2i2i−2i1-1-1i3−i3i3−i3100000002-200−iii−i−33−33i3−i3−ii−ii−33−33000000000-11i3−i30000000000
χ552-2-2-2222-2-1-222-211-111-1-1002i−2i−2i2i−2i2i−2i2i1-1-1−i3i3−i3i310000000-2200−iii−i3−33−3−i3i3i−ii−i−33−330000000001-1i3−i30000000000
χ562-2-2-2222-2-1-222-211-111-1-1002i−2i−2i2i−2i2i−2i2i1-1-1i3−i3i3−i310000000-2200−iii−i−33−33i3−i3i−ii−i3−33−30000000001-1−i3i30000000000
χ572-2-2-2222-2-1-222-211-111-1-100−2i2i2i−2i2i−2i2i−2i1-1-1−i3i3−i3i310000000-2200i−i−ii−33−33−i3i3−ii−ii3−33−30000000001-1i3−i30000000000
χ582-2-2-2222-2-1-222-211-111-1-100−2i2i2i−2i2i−2i2i−2i1-1-1i3−i3i3−i310000000-2200i−i−ii3−33−3i3−i3−ii−ii−33−330000000001-1−i3i30000000000
χ592-2-2-2222-2-1-222-211-111-1-100−2i2i2i−2i−2i2i−2i2i1-1-1−i3i3−i3i3100000002-200i−i−ii−33−33−i3i3i−ii−i−33−33000000000-11−i3i30000000000
χ602-2-2-2222-2-1-222-211-111-1-100−2i2i2i−2i−2i2i−2i2i1-1-1i3−i3i3−i3100000002-200i−i−ii3−33−3i3−i3i−ii−i3−33−3000000000-11i3−i30000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000222-2-2-2-22000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400000000222222220000004000000000000-2-20000000000000000000000000000000
χ63444-4-44-4-4-244-4-4-22-2-22220000000000-2-220000200004-4000000000-2-222000000000000000000000000000000000
χ64444-4-44-4-4-244-4-4-22-2-22220000000000-2-22000020000-4400000000022-2-2000000000000000000000000000000000
χ65444-4-44-4-4-2-4-444-22-2-2222004i4i−4i−4i000022-20000-200000000000−2i−2i2i2i0000000000000000000000000000000000000
χ66444-4-44-4-4-2-4-444-22-2-222200−4i−4i4i4i000022-20000-2000000000002i2i−2i−2i0000000000000000000000000000000000000
χ6744-444-4-4-44000044-4-4-4-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6844-444-4-4-44000044-4-4-4-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6944-4-4-4-444400004-4-4-444-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7044-4-4-4-444400004-4-4-444-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7144-4-4-4-444-20000-2222-2-2200000022−22−222200023−23−23230000000000000000000000−222−26−6−6600000000000000000000000
χ7244-4-4-4-444-20000-2222-2-2200000022−22−2222000−232323−230000000000000000000000−222−2−666−600000000000000000000000
χ7344-4-4-4-444-20000-2222-2-22000000−222222−2200023−23−232300000000000000000000002−2−22−666−600000000000000000000000
χ7444-4-4-4-444-20000-2222-2-22000000−222222−22000−232323−2300000000000000000000002−2−226−6−6600000000000000000000000
χ754-444-4-44-4-200002-22-22-224i−4i0000−2i2−2i22i22i2000−2i−2i2i2i000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ764-444-4-44-4-200002-22-22-224i−4i00002i22i2−2i2−2i2000−2i−2i2i2i0000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ774-444-4-44-4-200002-22-22-22−4i4i0000−2i2−2i22i22i20002i2i−2i−2i0000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ784-444-4-44-4-200002-22-22-22−4i4i00002i22i2−2i2−2i20002i2i−2i−2i000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ794-44-44-4-4440000-4-4-444-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ804-44-44-4-4440000-4-4-444-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ814-4-44-44-444-44-44-444-44-4-40000000000-44-4000040000000000000000000000000000000000000000000000000000
χ824-4-44-44-44-24-44-42-2-22-222004-44-40000-22-20000200000000000-22-220000000000000000000000000000000000000
χ834-4-44-44-44-24-44-42-2-22-22200-44-440000-22-200002000000000002-22-20000000000000000000000000000000000000
χ844-4-44-44-44-2-44-442-2-22-22200000000002-220000-200000000000000023−23−2323000000000000000000000000000000000
χ854-4-44-44-44-2-44-442-2-22-22200000000002-220000-2000000000000000−232323−23000000000000000000000000000000000
χ864-4-4-4444-444-4-44-4-44-4-44400000000004-4-4000040000000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-24-4-4422-222-2-20000000000-222−2i32i3−2i32i3-200000000000000000002i3−2i30000000000000000000000000000000
χ884-4-4-4444-4-24-4-4422-222-2-20000000000-2222i3−2i32i3−2i3-20000000000000000000−2i32i30000000000000000000000000000000
χ8988-888-8-8-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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