Finite Group Databasebeta

← Group #10693534

Character table — Group #10693534

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666444444444412121212121212128888888888881212121212121212121224242424242424248888888888884412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91-1-111-1-11111-11-1-11-1-1-1111-1-11-1ii−i−iii−i−i111-1-1-1-11iiii−i−i−i−i11-1-11-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1111-1-1-1-1i−iii−i−iii−i−i1-1
χ101-1-111-1-11111-11-1-11-1-1-1111-1-11-1ii−i−iii−i−i111-1-1-1-11iiii−i−i−i−i-1-1111-1ii−i−iii−i−i-1-1-1-11111ii−i−i1111-1-1-1-1−ii−i−iii−i−iii-11
χ111-1-111-1-11111-11-1-11-1-1-1111-1-11-1ii−i−iii−i−i111-1-1-1-11−i−i−i−iiiii11-1-11-1ii−i−iii−i−i1111-1-1-1-1−i−iii-1-1-1-11111i−iii−i−i−i−iii-11
χ121-1-111-1-11111-11-1-11-1-1-1111-1-11-1ii−i−iii−i−i111-1-1-1-11−i−i−i−iiiii-1-1111-1ii−i−iii−i−i-1-1-1-11111−i−iii-1-1-1-11111−ii−i−iiiii−i−i1-1
χ131-1-111-1-11111-11-1-11-1-1-1111-1-11-1−i−iii−i−iii111-1-1-1-11iiii−i−i−i−i11-1-11-1−i−iii−i−iii1111-1-1-1-1ii−i−i-1-1-1-11111−ii−i−iiiii−i−i-11
χ141-1-111-1-11111-11-1-11-1-1-1111-1-11-1−i−iii−i−iii111-1-1-1-11iiii−i−i−i−i-1-1111-1−i−iii−i−iii-1-1-1-11111ii−i−i-1-1-1-11111i−iii−i−i−i−iii1-1
χ151-1-111-1-11111-11-1-11-1-1-1111-1-11-1−i−iii−i−iii111-1-1-1-11−i−i−i−iiiii11-1-11-1−i−iii−i−iii1111-1-1-1-1−i−iii1111-1-1-1-1−ii−i−iii−i−iii1-1
χ161-1-111-1-11111-11-1-11-1-1-1111-1-11-1−i−iii−i−iii111-1-1-1-11−i−i−i−iiiii-1-1111-1−i−iii−i−iii-1-1-1-11111−i−iii1111-1-1-1-1i−iii−i−iii−i−i-11
χ172222222222-2-2-2222-22222222-2-20000000022-222-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ182222222222-2-2-2222-22222222-2-20000000022-222-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2222-2-2-222222222-2-22222-2-2-2-2-2-22-2-2222000000000000-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222-2222-2-2-222222222-2-2-2-2-2-22222-2-22-2-2222000000000000-2-2-2-2-2-2222200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-211-111-1-1-100000000000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-211-111-1-1-100000000000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2222211-111-1-1-1000000000000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2222211-111-1-1-1000000000000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ312222-2-2-2-2220002-2-20222-2-2-2-200000000002-202-200022-2-222-2-22−22−200000000002−22−22−22−20000000000000000002−22−200
χ322222-2-2-2-2220002-2-20222-2-2-2-200000000002-202-200022-2-222-2-2−22−220000000000−22−22−22−22000000000000000000−22−2200
χ332222-2-2-2-2220002-2-20222-2-2-2-200000000002-202-2000-2-222-2-2222−22−200000000002−22−22−22−2000000000000000000−22−2200
χ342222-2-2-2-2220002-2-20222-2-2-2-200000000002-202-2000-2-222-2-222−22−220000000000−22−22−22−220000000000000000002−22−200
χ3522-2-2-22-22202-2-200022-2-22-22-2002-22-20000002002-2-2−i2i2−i2i2−i2i2−i2i20000002-22-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-2-2-22-22202-2-200022-2-22-22-2002-22-20000002002-2-2i2−i2i2−i2i2−i2i2−i20000002-22-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3722-2-2-22-22202-2-200022-2-22-22-200-22-220000002002-2-2−i2i2−i2i2−i2i2−i2i2000000-22-22000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-2-22-22202-2-200022-2-22-22-200-22-220000002002-2-2i2−i2i2−i2i2−i2i2−i2000000-22-22000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-2-22-2220-222000-22-2-22-22-20000002i−2i2i−2i00-200-222−i2i2−i2i2−i2i2−i2i200000000002i−2i2i−2i00000000i2−i2i2−i22−2−222−2−22000000000000
χ4022-2-2-22-2220-222000-22-2-22-22-20000002i−2i2i−2i00-200-222i2−i2i2−i2i2−i2i2−i200000000002i−2i2i−2i00000000−i2i2−i2i2−222−2−222−2000000000000
χ4122-2-2-22-2220-222000-22-2-22-22-2000000−2i2i−2i2i00-200-222−i2i2−i2i2−i2i2−i2i20000000000−2i2i−2i2i00000000i2−i2i2−i2−222−2−222−2000000000000
χ4222-2-2-22-2220-222000-22-2-22-22-2000000−2i2i−2i2i00-200-222i2−i2i2−i2i2−i2i2−i20000000000−2i2i−2i2i00000000−i2i2−i2i22−2−222−2−22000000000000
χ432-22-2-2-2222022-2000-2-22-22-2-22002i−2i−2i2i000000200-22-22−22−2−22−220000002i−2i−2i2i0000000000002−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-2-2222022-2000-2-22-22-2-22002i−2i−2i2i000000200-22-2−22−222−22−20000002i−2i−2i2i000000000000−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-22-2-2-2222022-2000-2-22-22-2-2200−2i2i2i−2i000000200-22-22−22−2−22−22000000−2i2i2i−2i0000000000002−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ462-22-2-2-2222022-2000-2-22-22-2-2200−2i2i2i−2i000000200-22-2−22−222−22−2000000−2i2i2i−2i000000000000−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ472-22-2-2-22220-2-220002-22-22-2-220000002-2-2200-2002-222−22−2−22−2200000000002-2-2200000000−222−2−222−22−2−22000000000000
χ482-22-2-2-22220-2-220002-22-22-2-220000002-2-2200-2002-22−22−222−22−200000000002-2-22000000002−2−222−2−22−222−2000000000000
χ492-22-2-2-22220-2-220002-22-22-2-22000000-222-200-2002-222−22−2−22−220000000000-222-200000000−222−22−2−22−222−2000000000000
χ502-22-2-2-22220-2-220002-22-22-2-22000000-222-200-2002-22−22−222−22−20000000000-222-2000000002−2−22−222−22−2−22000000000000
χ512-2-222-2-2222-22-2-2-222-2-2222-2-2-220000000022-2-2-222-22i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ522-2-222-2-2222-22-2-2-222-2-2222-2-2-220000000022-2-2-222-2−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ532-2-222-2-222-22-2222-2-2-2-2222-2-2-222i2i−2i−2i−2i−2i2i2i-2-2222-2-22000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ542-2-222-2-222-22-2222-2-2-2-2222-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2222-2-22000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ552-2-222-2-222-2-22-222-22-2-2222-2-22-200000000-2-2-22222-20000000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ562-2-222-2-222-2-22-222-22-2-2222-2-22-200000000-2-2-22222-20000000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ572-2-222-2-22-122-22-2-22-211-1-1-1112-22i2i−2i−2i2i2i−2i−2i-1-1-11111-10000000022-2-2-11−i−iii−i−iii-1-1-1-111110000000000002i−2i−i−iii000000
χ582-2-222-2-22-122-22-2-22-211-1-1-1112-22i2i−2i−2i2i2i−2i−2i-1-1-11111-100000000-2-222-11−i−iii−i−iii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ592-2-222-2-22-122-22-2-22-211-1-1-1112-2−2i−2i2i2i−2i−2i2i2i-1-1-11111-10000000022-2-2-11ii−i−iii−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ602-2-222-2-22-122-22-2-22-211-1-1-1112-2−2i−2i2i2i−2i−2i2i2i-1-1-11111-100000000-2-222-11ii−i−iii−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ612-2-222-2-22-1-22-2222-2-211-1-1-111-222i2i−2i−2i−2i−2i2i2i11-1-1-111-10000000000001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000003−3−33000000
χ622-2-222-2-22-1-22-2222-2-211-1-1-111-222i2i−2i−2i−2i−2i2i2i11-1-1-111-10000000000001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000−333−3000000
χ632-2-222-2-22-1-22-2222-2-211-1-1-111-22−2i−2i2i2i2i2i−2i−2i11-1-1-111-10000000000001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000−333−3000000
χ642-2-222-2-22-1-22-2222-2-211-1-1-111-22−2i−2i2i2i2i2i−2i−2i11-1-1-111-10000000000001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000003−3−33000000
χ652-2-22-222-222000-22-20-2-22-2-22200000000002-20-220002i2i−2i−2i−2i−2i2i2i2−2−2200000000002−22−2−22−22000000000000000000i2−i2−i2i200
χ662-2-22-222-222000-22-20-2-22-2-22200000000002-20-220002i2i−2i−2i−2i−2i2i2i−222−20000000000−22−222−22−2000000000000000000−i2i2i2−i200
χ672-2-22-222-222000-22-20-2-22-2-22200000000002-20-22000−2i−2i2i2i2i2i−2i−2i2−2−2200000000002−22−2−22−22000000000000000000−i2i2i2−i200
χ682-2-22-222-222000-22-20-2-22-2-22200000000002-20-22000−2i−2i2i2i2i2i−2i−2i−222−20000000000−22−222−22−2000000000000000000i2−i2−i2i200
χ6944444444-24-4-4-4444-4-2-2-2-2-2-2-2-4-400000000-2-22-2-2222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ714444-4-4-4-44-4000-4440444-4-4-4-40000000000-440-44000000000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-240004-4-40-2-2-222220000000000-220-220000000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ734444-4-4-4-4-240004-4-40-2-2-222220000000000-220-2200000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ744444-4-4-4-4-2-4000-4440-2-2-2222200000000002-202-20000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ754444-4-4-4-4-2-4000-4440-2-2-2222200000000002-202-20000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ7644-4-44-44-44000000004-4-4-44-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ7744-4-44-44-44000000004-4-4-44-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ7844-4-4-44-44-204-4-40004-222-22-22004-44-4000000-200-22200000000000000-22-22000000000000000000000000000000000000
χ7944-4-4-44-44-204-4-40004-222-22-2200-44-44000000-200-222000000000000002-22-2000000000000000000000000000000000000
χ8044-4-4-44-44-20-444000-4-222-22-220000004i−4i4i−4i002002-2-2000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ8144-4-4-44-44-20-444000-4-222-22-22000000−4i4i−4i4i002002-2-20000000000000000002i−2i2i−2i00000000000000000000000000000000
χ824-44-444-4-4400000000-44-4-444-400000000000000000022−22−2222−222222−220000000000000000000000000000000000000000000000
χ834-44-444-4-4400000000-44-4-444-4000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000000000
χ844-44-4-4-444-2044-4000-42-22-222-2004i−4i−4i4i000000-2002-2200000000000000−2i2i2i−2i000000000000000000000000000000000000
χ854-44-4-4-444-2044-4000-42-22-222-200−4i4i4i−4i000000-2002-22000000000000002i−2i−2i2i000000000000000000000000000000000000
χ864-44-4-4-444-20-4-4400042-22-222-20000004-4-4400200-22-2000000000000000000-222-200000000000000000000000000000000
χ874-44-4-4-444-20-4-4400042-22-222-2000000-444-400200-22-20000000000000000002-2-2200000000000000000000000000000000
χ884-4-444-4-44-24-44-4-4-44422-2-2-222-4400000000-2-2222-2-220000000000002-20000000000000000000000000000000000000000
χ894-4-444-4-44-2-4-44-444-4422-2-2-2224-400000000222-2-2-2-22000000000000-220000000000000000000000000000000000000000
χ904-4-44-444-44-40004-440-4-44-4-4440000000000-4404-4000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-4-24000-44-4022-222-2-20000000000-2202-20000000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ924-4-44-444-4-24000-44-4022-222-2-20000000000-2202-200000000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ934-4-44-444-4-2-40004-44022-222-2-200000000002-20-220000000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ944-4-44-444-4-2-40004-44022-222-2-200000000002-20-220000000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ9588-8-88-88-8-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-888-8-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000

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