Finite Group Databasebeta

← Group #10855231

Character table — Group #10855231

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order1222222234444444466666664488888888121212121212121212121212242424242424242424242424242424244444222244442466121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1111-1-11-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-111-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1111-1-1-1-1
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11-11111-1-1-1-1-1-11-1-111-1-1-111
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-11111-1-1-1-111-111-1-1111-1-1
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-11-1-1-1-11111-1-1-1-1-111111-1-1
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-1-1111111111-1-1-1-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-11-1-11111-1-1111-1-1-1-1-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-111111-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-1111-111-1-1-1-11111-1-1-1-1-11-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11-111-1-1-1-111-1-111111-111-1-1
χ17222222222-22222-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000002222000000000000-20000-20000
χ18222222222-22222-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000002000020000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000022-2-2000000000000-2000020000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-22200000000000020000-20000
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
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-211-1-111-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000000022-1-111-1-111000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-1-1-11111000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-221111-1-1-1-1000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-200000000-2211-1-1-1-111000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-2-1-11111-1-1000000000000
χ292222-2-2-2-22-20000-2222-22-22-2-2002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i00000000000022-2-200000000000000000002i−2i00000
χ302222-2-2-2-22-20000-2222-22-22-2-2002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i000000000000-2-2220000000000000000000−2i2i00000
χ312222-2-2-2-22-20000-2222-22-22-2-200−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i00000000000022-2-20000000000000000000−2i2i00000
χ322222-2-2-2-22-20000-2222-22-22-2-200−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i000000000000-2-22200000000000000000002i−2i00000
χ3322-2-22-22-2202i2i−2i−2i00022-2-2-2-2200−i2i2−i2i222−2−2002i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−2000000002i−2i2-2000000000000000000−i2i22−2
χ3422-2-22-22-2202i2i−2i−2i00022-2-2-2-2200−i2i2−i2i222−2−2002i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−200000000−2i2i-22000000000000000000i2−i2−22
χ3522-2-22-22-2202i2i−2i−2i00022-2-2-2-2200i2−i2i2−i2−2−222002i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i2−2−2−2−22222000000002i−2i2-2000000000000000000i2−i2−22
χ3622-2-22-22-2202i2i−2i−2i00022-2-2-2-2200i2−i2i2−i2−2−222002i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i2−2−2−2−2222200000000−2i2i-22000000000000000000−i2i22−2
χ3722-2-22-22-220−2i−2i2i2i00022-2-2-2-2200−i2i2−i2i2−2−22200−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i2−2−2−2−22222000000002i−2i-22000000000000000000i2−i22−2
χ3822-2-22-22-220−2i−2i2i2i00022-2-2-2-2200−i2i2−i2i2−2−22200−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i2−2−2−2−2222200000000−2i2i2-2000000000000000000−i2i2−22
χ3922-2-22-22-220−2i−2i2i2i00022-2-2-2-2200i2−i2i2−i222−2−200−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−2000000002i−2i-22000000000000000000−i2i2−22
χ4022-2-22-22-220−2i−2i2i2i00022-2-2-2-2200i2−i2i2−i222−2−200−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−200000000−2i2i2-2000000000000000000i2−i22−2
χ412-22-222-2-2222i−2i2i−2i-2-22-222-2-22-22i−2i00000000-222i−2i2i−2i2i2i−2i−2i2-2000000000000000000002-22-2000000000000000002i−2i0000000
χ422-22-222-2-2222i−2i2i−2i-2-22-222-2-22-22i−2i00000000-222i−2i2i−2i2i2i−2i−2i2-200000000000000000000-22-2200000000000000000−2i2i0000000
χ432-22-222-2-222−2i2i−2i2i-2-22-222-2-22-2−2i2i00000000-22−2i2i−2i2i−2i−2i2i2i2-2000000000000000000002-22-200000000000000000−2i2i0000000
χ442-22-222-2-222−2i2i−2i2i-2-22-222-2-22-2−2i2i00000000-22−2i2i−2i2i−2i−2i2i2i2-200000000000000000000-22-22000000000000000002i−2i0000000
χ452-22-222-2-22-22i−2i2i−2i22-2-222-2-22-2−2i2i000000002-22i−2i2i−2i−2i−2i2i2i-2200000000000000002-22i−2i0000000000002-2002i−2i000000000000
χ462-22-222-2-22-22i−2i2i−2i22-2-222-2-22-2−2i2i000000002-22i−2i2i−2i−2i−2i2i2i-220000000000000000-22−2i2i000000000000-2200−2i2i000000000000
χ472-22-222-2-22-2−2i2i−2i2i22-2-222-2-22-22i−2i000000002-2−2i2i−2i2i2i2i−2i−2i-2200000000000000002-2−2i2i0000000000002-200−2i2i000000000000
χ482-22-222-2-22-2−2i2i−2i2i22-2-222-2-22-22i−2i000000002-2−2i2i−2i2i2i2i−2i−2i-220000000000000000-222i−2i000000000000-22002i−2i000000000000
χ492-22-222-2-2-1-22i−2i2i−2i22-21-1-111-11−2i2i00000000-11−ii−iiii−i−i1-1−i3i3−i3i3−i3i3−i3i333−3−333−3−32-22i−2i0000000000−i3i3-113−3−ii000000000000
χ502-22-222-2-2-1-22i−2i2i−2i22-21-1-111-11−2i2i00000000-11−ii−iiii−i−i1-1−i3i3−i3i3−i3i3−i3i333−3−333−3−3-22−2i2i0000000000i3−i31-1−33i−i000000000000
χ512-22-222-2-2-1-22i−2i2i−2i22-21-1-111-11−2i2i00000000-11−ii−iiii−i−i1-1i3−i3i3−i3i3−i3i3−i3−3−333−3−3332-22i−2i0000000000i3−i3-11−33−ii000000000000
χ522-22-222-2-2-1-22i−2i2i−2i22-21-1-111-11−2i2i00000000-11−ii−iiii−i−i1-1i3−i3i3−i3i3−i3i3−i3−3−333−3−333-22−2i2i0000000000−i3i31-13−3i−i000000000000
χ532-22-222-2-2-1-2−2i2i−2i2i22-21-1-111-112i−2i00000000-11i−ii−i−i−iii1-1−i3i3−i3i3−i3i3−i3i3−3−333−3−3332-2−2i2i0000000000−i3i3-11−33i−i000000000000
χ542-22-222-2-2-1-2−2i2i−2i2i22-21-1-111-112i−2i00000000-11i−ii−i−i−iii1-1−i3i3−i3i3−i3i3−i3i3−3−333−3−333-222i−2i0000000000i3−i31-13−3−ii000000000000
χ552-22-222-2-2-1-2−2i2i−2i2i22-21-1-111-112i−2i00000000-11i−ii−i−i−iii1-1i3−i3i3−i3i3−i3i3−i333−3−333−3−32-2−2i2i0000000000i3−i3-113−3i−i000000000000
χ562-22-222-2-2-1-2−2i2i−2i2i22-21-1-111-112i−2i00000000-11i−ii−i−i−iii1-1i3−i3i3−i3i3−i3i3−i333−3−333−3−3-222i−2i0000000000−i3i31-1−33−ii000000000000
χ572-22-2-2-2222-200002-22-2-222-2-220000002-22-2-2-20000000022000000002-22-22-22-200002-2-22000000000000002-20000000000
χ582-22-2-2-2222-200002-22-2-222-2-220000002-22-2-2-20000000022000000002-22-22-22-20000-222-200000000000000-220000000000
χ592-22-2-2-2222-200002-22-2-222-2-22000000-22-22-2-2000000002200000000-22-22-22-2200002-2-2200000000000000-220000000000
χ602-22-2-2-2222-200002-22-2-222-2-22000000-22-22-2-2000000002200000000-22-22-22-220000-222-2000000000000002-20000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ634444-4-4-4-44400004-4-44-44-44-4-40000000000-4400000000-4400000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2400004-4-4-22-22-22200000000002-2000000002-20000000023−23−232323−23−23230000000000000000000000000000000000
χ654444-4-4-4-4-2400004-4-4-22-22-22200000000002-2000000002-200000000−232323−23−232323−230000000000000000000000000000000000
χ664444-4-4-4-4-2-40000-444-22-22-222004i4i−4i−4i0000-2200000000-22−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000
χ674444-4-4-4-4-2-40000-444-22-22-22200−4i−4i4i4i0000-2200000000-222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000
χ6844-4-44-44-4-204i4i−4i−4i000-2-22222-200−2i22i2−2i22i22222−22−2200−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i2−2−2−2−222220000000000000000000000000000000000
χ6944-4-44-44-4-204i4i−4i−4i000-2-22222-2002i2−2i22i2−2i2−22−22222200−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−20000000000000000000000000000000000
χ7044-4-44-44-4-20−4i−4i4i4i000-2-22222-200−2i22i2−2i22i2−22−222222002i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−20000000000000000000000000000000000
χ7144-4-44-44-4-20−4i−4i4i4i000-2-22222-2002i2−2i22i2−2i22222−22−22002i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i2−2−2−2−222220000000000000000000000000000000000
χ7244-4-4-44-444000000004-4-44-44-40022−22−222200000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ7344-4-4-44-444000000004-4-44-44-400−222222−220000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ7444-4-4-44-44-200000000-222-22-220022−22−2222000000000023−2323−2300−2−22222−2−26−6−66−666−60000000000000000000000000000000000
χ7544-4-4-44-44-200000000-222-22-220022−22−22220000000000−2323−232300−2−22222−2−2−666−66−6−660000000000000000000000000000000000
χ7644-4-4-44-44-200000000-222-22-2200−222222−22000000000023−2323−230022−2−2−2−222−666−66−6−660000000000000000000000000000000000
χ7744-4-4-44-44-200000000-222-22-2200−222222−220000000000−2323−23230022−2−2−2−2226−6−66−666−60000000000000000000000000000000000
χ784-44-444-4-4-244i−4i4i−4i-4-442-2-222-224i−4i000000002-2−2i2i−2i2i−2i−2i2i2i-2200000000000000000000000000000000000000000000000000
χ794-44-444-4-4-24−4i4i−4i4i-4-442-2-222-22−4i4i000000002-22i−2i2i−2i2i2i−2i−2i-2200000000000000000000000000000000000000000000000000
χ804-44-4-4-444440000-44-4-4-444-4-4400000000004400000000-4-400000000000000000000000000000000000000000000000000
χ814-44-4-4-444-240000-44-422-2-222-20000000000-2-2000000002223−2323−23−2323−2323000000000000000000000000000000000000000000
χ824-44-4-4-444-240000-44-422-2-222-20000000000-2-20000000022−2323−232323−2323−23000000000000000000000000000000000000000000
χ834-44-4-4-444-2-400004-4422-2-222-20000004-44-42200000000-2-200000000-22-22-22-220000000000000000000000000000000000
χ844-44-4-4-444-2-400004-4422-2-222-2000000-44-442200000000-2-2000000002-22-22-22-20000000000000000000000000000000000
χ854-4-444-4-44404-4-44000-44-444-4-40000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ864-4-444-4-4440-444-4000-44-444-4-4000000000000-444-400000000000000000000000000000000000000000000000000000000
χ874-4-444-4-44-204-4-440002-22-2-222000000000000-222-20000006−6−666−6−6666−6−6−6−6660000000000000000000000000000000000
χ884-4-444-4-44-204-4-440002-22-2-222000000000000-222-2000000−666−6−666−6−6−66666−6−60000000000000000000000000000000000
χ894-4-444-4-44-20-444-40002-22-2-2220000000000002-2-220000006−6−666−6−66−6−66666−6−60000000000000000000000000000000000
χ904-4-444-4-44-20-444-40002-22-2-2220000000000002-2-22000000−666−6−666−666−6−6−6−6660000000000000000000000000000000000
χ914-4-44-444-4400000000-4-4-4-444400000022−22−22220000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ924-4-44-444-4400000000-4-4-4-4444000000−222222−2200000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ934-4-44-444-4-2000000002222-2-2-200000022−22−2222000000−2i32i32i3−2i300i6−i6−i6i6−i6i6i6−i6−22−222−22−20000000000000000000000000000000000
χ944-4-44-444-4-2000000002222-2-2-200000022−22−22220000002i3−2i3−2i32i300−i6i6i6−i6i6−i6−i6i6−22−222−22−20000000000000000000000000000000000
χ954-4-44-444-4-2000000002222-2-2-2000000−222222−22000000−2i32i32i3−2i300−i6i6i6−i6i6−i6−i6i62−22−2−22−220000000000000000000000000000000000
χ964-4-44-444-4-2000000002222-2-2-2000000−222222−220000002i3−2i3−2i32i300i6−i6−i6i6−i6i6i6−i62−22−2−22−220000000000000000000000000000000000

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