Finite Group Databasebeta

← Group #10868060

Character table — Group #10868060

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444444444444441212121212121212244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1-1-1-111-11-1-111-1-111-1-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-1111-111-1-111-1-111
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-11111-1-11-1-1-111-1-1-1-111
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-1-11111-1-1-1111-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111111-1-11-11111-1-1-1-1-1111-1-1-1-1-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-11-1-1-1-111111-111-1-1-1-111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-11-1-1-1-11111-11-1-11111-1-111
χ172222222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000000022220000000000-2-20000000000
χ182222222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-2-2-20000000000220000000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-22222-2-2-2-2-2-200000000000000000000000022-2-200000000002-20000000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2000000000000000000000000-2-2220000000000-220000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-111-1-111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000000002211-1-111-1-1000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200000000-22-1-11111-1-1000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-222000000002-211-1-1-1-111000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-2000000002-2-1-1-1-11111000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-22200000000-221111-1-1-1-1000000000000
χ292222-2-2-2-2222-2-200002-2-2-2-2220022−2−222−2−200000022-2-2002222−2−2−2−22222−2−2−2−2000000002i−2i2i−2i000000000000000000−i2i2−i2i2
χ302222-2-2-2-2222-2-200002-2-2-2-2220022−2−222−2−200000022-2-2002222−2−2−2−22222−2−2−2−200000000−2i2i−2i2i000000000000000000i2−i2i2−i2
χ312222-2-2-2-2222-2-200002-2-2-2-22200−2−222−2−22200000022-2-200−2−2−2−22222−2−2−2−22222000000002i−2i2i−2i000000000000000000i2−i2i2−i2
χ322222-2-2-2-2222-2-200002-2-2-2-22200−2−222−2−22200000022-2-200−2−2−2−22222−2−2−2−2222200000000−2i2i−2i2i000000000000000000−i2i2−i2i2
χ332222-2-2-2-22-2-22200002-2-2-2-2220022−2−2−2−222000000-2-222002222−2−2−2−2−2−2−2−22222000000002i−2i−2i2i000000000000000000−i2i2i2−i2
χ342222-2-2-2-22-2-22200002-2-2-2-2220022−2−2−2−222000000-2-222002222−2−2−2−2−2−2−2−2222200000000−2i2i2i−2i000000000000000000i2−i2−i2i2
χ352222-2-2-2-22-2-22200002-2-2-2-22200−2−22222−2−2000000-2-22200−2−2−2−222222222−2−2−2−2000000002i−2i−2i2i000000000000000000i2−i2−i2i2
χ362222-2-2-2-22-2-22200002-2-2-2-22200−2−22222−2−2000000-2-22200−2−2−2−222222222−2−2−2−200000000−2i2i2i−2i000000000000000000−i2i2i2−i2
χ3722-2-2-2-22220000-2-22222-22-2-2-20000002-22-22-2000000002-20000000022-2-222-2-200002i2i−2i−2i00000000000000002i−2i00000000
χ3822-2-2-2-22220000-2-22222-22-2-2-20000002-22-22-2000000002-20000000022-2-222-2-20000−2i−2i2i2i0000000000000000−2i2i00000000
χ3922-2-2-2-22220000-2-22222-22-2-2-2000000-22-222-2000000002-200000000-2-222-2-22200002i2i−2i−2i0000000000000000−2i2i00000000
χ4022-2-2-2-22220000-2-22222-22-2-2-2000000-22-222-2000000002-200000000-2-222-2-2220000−2i−2i2i2i00000000000000002i−2i00000000
χ412-22-22-2-2222i−2i2i−2i2-2-22-2-222-22-22i−2i00000000-222i2i−2i−2i2i−2i2i−2i2-200000000000000002-22i−2i00000000002-2002i−2i00000000000000
χ422-22-22-2-2222i−2i2i−2i2-2-22-2-222-22-22i−2i00000000-222i2i−2i−2i2i−2i2i−2i2-20000000000000000-22−2i2i0000000000-2200−2i2i00000000000000
χ432-22-22-2-2222i−2i2i−2i-222-2-2-222-22-2−2i2i000000002-2−2i−2i2i2i2i−2i2i−2i-22000000000000000000002i−2i2i−2i000000000000000000002-20000
χ442-22-22-2-2222i−2i2i−2i-222-2-2-222-22-2−2i2i000000002-2−2i−2i2i2i2i−2i2i−2i-2200000000000000000000−2i2i−2i2i00000000000000000000-220000
χ452-22-22-2-222−2i2i−2i2i2-2-22-2-222-22-2−2i2i00000000-22−2i−2i2i2i−2i2i−2i2i2-200000000000000002-2−2i2i00000000002-200−2i2i00000000000000
χ462-22-22-2-222−2i2i−2i2i2-2-22-2-222-22-2−2i2i00000000-22−2i−2i2i2i−2i2i−2i2i2-20000000000000000-222i−2i0000000000-22002i−2i00000000000000
χ472-22-22-2-222−2i2i−2i2i-222-2-2-222-22-22i−2i000000002-22i2i−2i−2i−2i2i−2i2i-22000000000000000000002i−2i2i−2i00000000000000000000-220000
χ482-22-22-2-222−2i2i−2i2i-222-2-2-222-22-22i−2i000000002-22i2i−2i−2i−2i2i−2i2i-2200000000000000000000−2i2i−2i2i000000000000000000002-20000
χ492-22-22-2-22-12i−2i2i−2i2-2-2211-1-11-112i−2i000000001-1−i−iii−ii−ii-1133−3−333−3−3−i3i3−i3i3−i3i3−i3i32-22i−2i0000000000-11−i3i3−ii3−3000000000000
χ502-22-22-2-22-12i−2i2i−2i2-2-2211-1-11-112i−2i000000001-1−i−iii−ii−ii-1133−3−333−3−3−i3i3−i3i3−i3i3−i3i3-22−2i2i00000000001-1i3−i3i−i−33000000000000
χ512-22-22-2-22-12i−2i2i−2i2-2-2211-1-11-112i−2i000000001-1−i−iii−ii−ii-11−3−333−3−333i3−i3i3−i3i3−i3i3−i32-22i−2i0000000000-11i3−i3−ii−33000000000000
χ522-22-22-2-22-12i−2i2i−2i2-2-2211-1-11-112i−2i000000001-1−i−iii−ii−ii-11−3−333−3−333i3−i3i3−i3i3−i3i3−i3-22−2i2i00000000001-1−i3i3i−i3−3000000000000
χ532-22-22-2-22-1−2i2i−2i2i2-2-2211-1-11-11−2i2i000000001-1ii−i−ii−ii−i-1133−3−333−3−3i3−i3i3−i3i3−i3i3−i32-2−2i2i0000000000-11i3−i3i−i3−3000000000000
χ542-22-22-2-22-1−2i2i−2i2i2-2-2211-1-11-11−2i2i000000001-1ii−i−ii−ii−i-1133−3−333−3−3i3−i3i3−i3i3−i3i3−i3-222i−2i00000000001-1−i3i3−ii−33000000000000
χ552-22-22-2-22-1−2i2i−2i2i2-2-2211-1-11-11−2i2i000000001-1ii−i−ii−ii−i-11−3−333−3−333−i3i3−i3i3−i3i3−i3i32-2−2i2i0000000000-11−i3i3i−i−33000000000000
χ562-22-22-2-22-1−2i2i−2i2i2-2-2211-1-11-11−2i2i000000001-1ii−i−ii−ii−i-11−3−333−3−333−i3i3−i3i3−i3i3−i3i3-222i−2i00000000001-1i3−i3−ii3−3000000000000
χ572-2-22-22-22200002-22-2-2-2-222-22002i−2i2i−2i00002200000000-2-22i−2i2i−2i2i−2i2i−2i0000000000002-2-220000000000000000002i−2i000000
χ582-2-22-22-22200002-22-2-2-2-222-22002i−2i2i−2i00002200000000-2-22i−2i2i−2i2i−2i2i−2i000000000000-222-2000000000000000000−2i2i000000
χ592-2-22-22-22200002-22-2-2-2-222-2200−2i2i−2i2i00002200000000-2-2−2i2i−2i2i−2i2i−2i2i0000000000002-2-22000000000000000000−2i2i000000
χ602-2-22-22-22200002-22-2-2-2-222-2200−2i2i−2i2i00002200000000-2-2−2i2i−2i2i−2i2i−2i2i000000000000-222-20000000000000000002i−2i000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-40000-22222-2-2002222−22−222222−22−22000000-2-22200−2−2−2−22222−2−2−2−222220000000000000000000000000000000000
χ644444-4-4-4-4-244-4-40000-22222-2-200−22−222222−22−222222000000-2-222002222−2−2−2−22222−2−2−2−20000000000000000000000000000000000
χ654444-4-4-4-4-2-4-4440000-22222-2-2002222−22−22−22−22222200000022-2-200−2−2−2−222222222−2−2−2−20000000000000000000000000000000000
χ664444-4-4-4-4-2-4-4440000-22222-2-200−22−2222222222−22−2200000022-2-2002222−2−2−2−2−2−2−2−222220000000000000000000000000000000000
χ6744-4-444-4-44000000004-44-44-4-400000022−22−2222000000000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ6844-4-444-4-44000000004-44-44-4-4000000−222222−2200000000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ6944-4-444-4-4-200000000-22-22-22200000022−22−222200−2i32i3−2i32i3000000i6−i6−i6i6−i6i6i6−i6−2−22222−2−20000000000000000000000000000000000
χ7044-4-444-4-4-200000000-22-22-22200000022−22−2222002i3−2i32i3−2i3000000−i6i6i6−i6i6−i6−i6i6−2−22222−2−20000000000000000000000000000000000
χ7144-4-444-4-4-200000000-22-22-222000000−222222−2200−2i32i3−2i32i3000000−i6i6i6−i6i6−i6−i6i622−2−2−2−2220000000000000000000000000000000000
χ7244-4-444-4-4-200000000-22-22-222000000−222222−22002i3−2i32i3−2i3000000i6−i6−i6i6−i6i6i6−i622−2−2−2−2220000000000000000000000000000000000
χ7344-4-4-4-4444000044-4-444-44-4-4-40000000000-4400000000-4400000000000000000000000000000000000000000000000000
χ7444-4-4-4-444-2000044-4-4-2-22-222200000000002-2000000002-2−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000
χ7544-4-4-4-444-2000044-4-4-2-22-222200000000002-2000000002-22i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000
χ7644-4-4-4-444-20000-4-444-2-22-22220000004-44-4-2200000000-2200000000-2-222-2-2220000000000000000000000000000000000
χ7744-4-4-4-444-20000-4-444-2-22-2222000000-44-44-2200000000-220000000022-2-222-2-20000000000000000000000000000000000
χ784-44-44-4-44-24i−4i4i−4i-444-422-2-22-22−4i4i00000000-222i2i−2i−2i−2i2i−2i2i2-200000000000000000000000000000000000000000000000000
χ794-44-44-4-44-2−4i4i−4i4i-444-422-2-22-224i−4i00000000-22−2i−2i2i2i2i−2i2i−2i2-200000000000000000000000000000000000000000000000000
χ804-44-4-444-444i−4i−4i4i0000-44-4-444-400000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ814-44-4-444-44−4i4i4i−4i0000-44-4-444-40000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ824-44-4-444-4-24i−4i−4i4i00002-222-2-220000000000000000−2i2i2i−2i0066−6−6−6−666−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ834-44-4-444-4-24i−4i−4i4i00002-222-2-220000000000000000−2i2i2i−2i00−6−66666−6−6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000
χ844-44-4-444-4-2−4i4i4i−4i00002-222-2-2200000000000000002i−2i−2i2i0066−6−6−6−666i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000
χ854-44-4-444-4-2−4i4i4i−4i00002-222-2-2200000000000000002i−2i−2i2i00−6−66666−6−6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ864-4-444-44-4400000000-444-4-4-4400−2i22i22i2−2i20000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ874-4-444-44-4400000000-444-4-4-44002i2−2i2−2i22i200000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ884-4-444-44-4-2000000002-2-2222-200−2i22i22i2−2i200000023−23−2323000000i2−i2i2−i2−i2i2−i2i2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ894-4-444-44-4-2000000002-2-2222-200−2i22i22i2−2i2000000−232323−23000000i2−i2i2−i2−i2i2−i2i2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ904-4-444-44-4-2000000002-2-2222-2002i2−2i2−2i22i200000023−23−2323000000−i2i2−i2i2i2−i2i2−i2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ914-4-444-44-4-2000000002-2-2222-2002i2−2i2−2i22i2000000−232323−23000000−i2i2−i2i2i2−i2i2−i2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ924-4-44-44-4440000-44-44-4-4-444-440000000000-4-4000000004400000000000000000000000000000000000000000000000000
χ934-4-44-44-44-200004-44-4222-2-22-2004i−4i4i−4i0000-2-20000000022−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ944-4-44-44-44-200004-44-4222-2-22-200−4i4i−4i4i0000-2-200000000222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000
χ954-4-44-44-44-20000-44-44222-2-22-200000000002200000000-2-200000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000
χ964-4-44-44-44-20000-44-44222-2-22-200000000002200000000-2-2000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000

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