Finite Group Databasebeta

← Group #10945109

Character table — Group #10945109

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222344444444666666622224444441212121212121212444444446666888812121212121224242424242424244444444444444412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-11-1
χ10111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-11-1-111-1-111-11
χ11111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-11
χ12111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-11-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-11-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-11-111-1-111-1-1-11
χ172222222222222-2-2-2-2222222200000000-2-22222-2-2-2-22222222200000000-2-2000000000000-2-2-2-200000000000000000000
χ182222222222222-2-2-2-2222222200000000-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2000000000000222200000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222220000000022-2-2-2-2-2-2-2-22222-2-2-2-20000000022000000000000-2-22200000000000000000000
χ20222222222-2-2-2-2-2-2-2-222222220000000022-2-2-2-2-2-2-2-2-2-2-2-22222000000002200000000000022-2-200000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-10000000011112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1000000001111-2-2-2-2-1-111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-100000000-1-1-1-122-2-2111111-1-1-1-111110000000000002-2-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-100000000-1-1-1-1-2-2221111111111-1-1-1-1000000000000-2211-1-1000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-22222-2-21111-1-1-1-100000000111122-2-211-1-1-1-1-1-1-1-11111000000000000-2211-1-1000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-22222-2-21111-1-1-1-1000000001111-2-22211-1-1-1-11111-1-1-1-10000000000002-2-1-111000000
χ2922-2-222-2-2200002-22-222-2-2-2-2222-2-200000000002-2-2200002i2i−2i−2i22-2-2000000000000000000002i−2i00002i2i−2i−2i000000000000
χ3022-2-222-2-2200002-22-222-2-2-2-2222-2-200000000002-2-220000−2i−2i2i2i22-2-200000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ3122-2-222-2-2200002-22-222-2-2-2-22-2-22200000000002-2-2200002i2i−2i−2i-2-222000000000000000000002i−2i0000−2i−2i2i2i000000000000
χ3222-2-222-2-2200002-22-222-2-2-2-22-2-22200000000002-2-220000−2i−2i2i2i-2-22200000000000000000000−2i2i00002i2i−2i−2i000000000000
χ3322-2-222-2-220000-22-2222-2-2-2-2200002i2i−2i−2i000000-222-200002i2i−2i−2i00000000002i2i−2i−2i0000000000−2i2i22-2-20000000000000000
χ3422-2-222-2-220000-22-2222-2-2-2-2200002i2i−2i−2i000000-222-20000−2i−2i2i2i00000000002i2i−2i−2i00000000002i−2i-2-2220000000000000000
χ3522-2-222-2-220000-22-2222-2-2-2-220000−2i−2i2i2i000000-222-200002i2i−2i−2i0000000000−2i−2i2i2i0000000000−2i2i-2-2220000000000000000
χ3622-2-222-2-220000-22-2222-2-2-2-220000−2i−2i2i2i000000-222-20000−2i−2i2i2i0000000000−2i−2i2i2i00000000002i−2i22-2-20000000000000000
χ372-22-22-22-2200002-2-22-2-222-2-2200002i−2i2i−2i00000022-2-22i2i−2i−2i000000000000002i−2i2i−2i000000002i−2i0000002-22-2000000000000
χ382-22-22-22-2200002-2-22-2-222-2-2200002i−2i2i−2i00000022-2-2−2i−2i2i2i000000000000002i−2i2i−2i00000000−2i2i000000-22-22000000000000
χ392-22-22-22-2200002-2-22-2-222-2-220000−2i2i−2i2i00000022-2-22i2i−2i−2i00000000000000−2i2i−2i2i000000002i−2i000000-22-22000000000000
χ402-22-22-22-2200002-2-22-2-222-2-220000−2i2i−2i2i00000022-2-2−2i−2i2i2i00000000000000−2i2i−2i2i00000000−2i2i0000002-22-2000000000000
χ412-22-22-22-220000-222-2-2-222-2-222-22-20000000000-2-2222i2i−2i−2i00002-22-2000000000000000000−2i2i002i−2i2i−2i0000000000000000
χ422-22-22-22-220000-222-2-2-222-2-222-22-20000000000-2-222−2i−2i2i2i00002-22-20000000000000000002i−2i00−2i2i−2i2i0000000000000000
χ432-22-22-22-220000-222-2-2-222-2-22-22-220000000000-2-2222i2i−2i−2i0000-22-22000000000000000000−2i2i00−2i2i−2i2i0000000000000000
χ442-22-22-22-220000-222-2-2-222-2-22-22-220000000000-2-222−2i−2i2i2i0000-22-220000000000000000002i−2i002i−2i2i−2i0000000000000000
χ452-2-222-2-22222-2-222-2-2-2-2-2-2222000000002-222-2-22-22-200000000000000002-200000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ462-2-222-2-22222-2-222-2-2-2-2-2-2222000000002-222-2-22-22-200000000000000002-20000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ472-2-222-2-22222-2-2-2-222-2-2-2-22222-2-22-222-2-2222-2-2-22-22000000002-2-220000-22-222-200000000000000000000000000000000
χ482-2-222-2-22222-2-2-2-222-2-2-2-2222-222-22-2-22-2222-2-2-22-2200000000-222-20000-222-2-2200000000000000000000000000000000
χ492-2-222-2-222-2-22222-2-2-2-2-2-222200000000-22-2-2222-22-20000000000000000-2200000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ502-2-222-2-222-2-22222-2-2-2-2-2-222200000000-22-2-2222-22-20000000000000000-220000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ512-2-222-2-222-2-222-2-222-2-2-2-22222-2-222-2-222-2-2-222-22-22000000002-2-2200002-22-2-2200000000000000000000000000000000
χ522-2-222-2-222-2-222-2-222-2-2-2-2222-222-2-222-22-2-2-222-22-2200000000-222-200002-2-222-200000000000000000000000000000000
χ532-2-222-2-22-122-2-2-2-2221111-1-1-12-2-22-222-2-22-1-1111-11-100000000-111-100001-11-1-11−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ542-2-222-2-22-122-2-2-2-2221111-1-1-12-2-22-222-2-22-1-1111-11-100000000-111-100001-11-1-11i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ552-2-222-2-22-122-2-2-2-2221111-1-1-1-222-22-2-22-22-1-1111-11-1000000001-1-1100001-1-111-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ562-2-222-2-22-122-2-2-2-2221111-1-1-1-222-22-2-22-22-1-1111-11-1000000001-1-1100001-1-111-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ572-2-222-2-22-1-2-222-2-2221111-1-1-12-2-222-2-222-211-1-11-11-100000000-111-10000-11-111-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ582-2-222-2-22-1-2-222-2-2221111-1-1-12-2-222-2-222-211-1-11-11-100000000-111-10000-11-111-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ592-2-222-2-22-1-2-222-2-2221111-1-1-1-222-2-222-22-211-1-11-11-1000000001-1-110000-111-1-11−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ602-2-222-2-22-1-2-222-2-2221111-1-1-1-222-2-222-22-211-1-11-11-1000000001-1-110000-111-1-11i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ612-2-22-222-222-22-200002-22-2-22-200000000002-22-200002-22-22-22-20000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i200
χ622-2-22-222-222-22-200002-22-2-22-200000000002-22-200002-22-22-22-20000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i200
χ632-2-22-222-222-22-200002-22-2-22-200000000002-22-20000-22-22-22-220000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i2i2−i200
χ642-2-22-222-222-22-200002-22-2-22-200000000002-22-20000-22-22-22-220000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2−i2i200
χ652-2-22-222-22-22-2200002-22-2-22-20000000000-22-2200002-22-2-22-220000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2000000000000000000−i2i2i2−i200
χ662-2-22-222-22-22-2200002-22-2-22-20000000000-22-2200002-22-2-22-220000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2000000000000000000i2−i2−i2i200
χ672-2-22-222-22-22-2200002-22-2-22-20000000000-22-220000-22-222-22-20000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2000000000000000000i2−i2−i2i200
χ682-2-22-222-22-22-2200002-22-2-22-20000000000-22-220000-22-222-22-20000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2000000000000000000−i2i2i2−i200
χ6944444444-24444-4-4-4-4-2-2-2-2-2-2-200000000-4-4-2-2-2-22222000000000000000022000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-20000000044222222220000000000000000-2-2000000000000000000000000000000000000
χ714444-4-4-4-444-4-440000-44-44-44-400000000004-4-440000000000000000000000000000000000000000000000000000000000
χ724444-4-4-4-44-444-40000-44-44-44-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-24-4-4400002-22-22-220000000000-222-2000000000000000000000000006−6−666−6−66000000000000000000000000
χ744444-4-4-4-4-24-4-4400002-22-22-220000000000-222-200000000000000000000000000−666−6−666−6000000000000000000000000
χ754444-4-4-4-4-2-444-400002-22-22-2200000000002-2-22000000000000000000000000006−6−66−666−6000000000000000000000000
χ764444-4-4-4-4-2-444-400002-22-22-2200000000002-2-2200000000000000000000000000−666−66−6−66000000000000000000000000
χ7744-4-444-4-4-200004-44-4-2-22222-244-4-40000000000-222-200000000-2-222000000000000000000000000000000000000000000
χ7844-4-444-4-4-200004-44-4-2-22222-2-4-4440000000000-222-20000000022-2-2000000000000000000000000000000000000000000
χ7944-4-444-4-4-20000-44-44-2-22222-200004i4i−4i−4i0000002-2-22000000000000000000−2i−2i2i2i00000000000000000000000000000000
χ8044-4-444-4-4-20000-44-44-2-22222-20000−4i−4i4i4i0000002-2-220000000000000000002i2i−2i−2i00000000000000000000000000000000
χ8144-4-4-4-444400000000-444-44-4-40000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ8244-4-4-4-444400000000-444-44-4-4000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ834-44-44-44-4-200004-4-4422-2-222-200004i−4i4i−4i000000-2-222000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ844-44-44-44-4-200004-4-4422-2-222-20000−4i4i−4i4i000000-2-2220000000000000000002i−2i2i−2i00000000000000000000000000000000
χ854-44-44-44-4-20000-444-422-2-222-24-44-4000000000022-2-200000000-22-22000000000000000000000000000000000000000000
χ864-44-44-44-4-20000-444-422-2-222-2-44-44000000000022-2-2000000002-22-2000000000000000000000000000000000000000000
χ874-44-4-44-444000000004-4-444-4-400000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ884-44-4-44-444000000004-4-444-4-40000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ894-4-444-4-44-244-4-444-4-42222-2-2-2000000004-4-2-222-22-220000000000000000-22000000000000000000000000000000000000
χ904-4-444-4-44-2-4-44444-4-42222-2-2-200000000-4422-2-2-22-2200000000000000002-2000000000000000000000000000000000000
χ914-4-44-444-4-24-44-40000-22-222-220000000000-22-220000000000000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ924-4-44-444-4-24-44-40000-22-222-220000000000-22-2200000000000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ934-4-44-444-4-2-44-440000-22-222-2200000000002-22-20000000000000000−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ944-4-44-444-4-2-44-440000-22-222-2200000000002-22-200000000000000002i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ9588-8-8-8-888-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-88-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000000000

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