Finite Group Databasebeta

← Group #10770419

Character table — Group #10770419

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222244444444488888888888888888888161616161616161616162424242424242424242424244848
order122222344666666644444121212124444444412121212121212121212121244121212121212121224444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1111111-1-1
χ91111111-1-11111111-1-1-111-1-1-1-11-11-111-1-11111-1-1-1-111-1-11-11-11-111-1-111-11-1-11-111-1-11-1
χ101111111-1-11111111-1-1-111-1-1-1-11-11-111-1-11111-1-1-1-111-1-11-11-11-111-1-1-1-11-111-11-1-111-11
χ111111111-1-11111111-1-1-111-1-1-1-11-11-1-1-111-1-1-1-1111111-1-1-111-11-1-1-11111-11-1-11-1-1-111-11
χ121111111-1-11111111-1-1-111-1-1-1-11-11-1-1-111-1-1-1-1111111-1-1-111-11-1-1-111-1-11-111-1111-1-11-1
χ131111111-1-11111111-1-1-111-1-1-1-1-11-1111-1-11111-1-1-1-111-1-1-11-11-11-1-11111-1-11-1-1111-1-1-11
χ141111111-1-11111111-1-1-111-1-1-1-1-11-1111-1-11111-1-1-1-111-1-1-11-11-11-1-111-1-111-111-1-1-1111-1
χ151111111-1-11111111-1-1-111-1-1-1-1-11-11-1-111-1-1-1-1111111-1-11-1-11-1111-1-111-1-11-1-11-1-1111-1
χ161111111-1-11111111-1-1-111-1-1-1-1-11-11-1-111-1-1-1-1111111-1-11-1-11-1111-1-1-1-111-111-111-1-1-11
χ1722222222222222222-2-2-2-2222222-2-2000000000000-2-2-2-200-2-222000000000000000000
χ1822222222222222222-2-2-2-22222-2-222000000000000-2-2-2-20022-2-2000000000000000000
χ192222222-2-22222222-222-2-2-2-2-2-22-2-22000000000000-2-22200-222-2000000000000000000
χ202222222-2-22222222-222-2-2-2-2-2-2-222-2000000000000-2-222002-2-22000000000000000000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-12222-2-2-2-211111111-1-1-1-1-2-2-1-1-1-1111100000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1221111-1-1-1-100000000000000
χ25222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-122-2-20000−i3−i3i3i3−i3−i3i3i311110011-1-1−i3i3−i3i300000000000000
χ26222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-122-2-20000i3i3−i3−i3i3i3−i3−i311110011-1-1i3−i3i3−i300000000000000
χ27222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-2-2220000−i3−i3i3i3−i3−i3i3i3111100-1-111i3−i3i3−i300000000000000
χ28222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-2-2220000i3i3−i3−i3i3i3−i3−i3111100-1-111−i3i3−i3i300000000000000
χ29222222-1-2-2-1-1-1-1-1-1-1-222-2-211112-2-220000−i3−i3i3i3i3i3−i3−i311-1-1001-1-11−i3i3i3−i300000000000000
χ30222222-1-2-2-1-1-1-1-1-1-1-222-2-211112-2-220000i3i3−i3−i3−i3−i3i3i311-1-1001-1-11i3−i3−i3i300000000000000
χ31222222-1-2-2-1-1-1-1-1-1-1-222-2-21111-222-20000−i3−i3i3i3i3i3−i3−i311-1-100-111-1i3−i3−i3i300000000000000
χ32222222-1-2-2-1-1-1-1-1-1-1-222-2-21111-222-20000i3i3−i3−i3−i3−i3i3i311-1-100-111-1−i3i3i3−i300000000000000
χ33222222-1-2-2-1-1-1-1-1-1-1-2-2-22211112-22-222-2-2-1-1-1-11111-1-1112-2-11-11-1-11100000000000000
χ34222222-1-2-2-1-1-1-1-1-1-1-2-2-22211112-22-2-2-2221111-1-1-1-1-1-111-22-11-1111-1-100000000000000
χ35222222-1-2-2-1-1-1-1-1-1-1-2-2-2221111-22-2222-2-2-1-1-1-11111-1-111-221-11-111-1-100000000000000
χ36222222-1-2-2-1-1-1-1-1-1-1-2-2-2221111-22-22-2-2221111-1-1-1-1-1-1112-21-11-1-1-11100000000000000
χ372222-2-22222-2-2-2-222-22-22-222-2-200000000000000002-22-20000000000000220-2-2000000
χ382222-2-22222-2-2-2-222-22-22-222-2-200000000000000002-22-20000000000000-2-2022000000
χ392222-2-22222-2-2-2-222-2-22-2222-2-20000000000000000-22-2200000000002-2200-200000000
χ402222-2-22222-2-2-2-222-2-22-2222-2-20000000000000000-22-220000000000-22-200200000000
χ412222-2-22-2-22-2-2-2-22222-2-22-2-2220000000000000000-222-200000000002-2-200200000000
χ422222-2-22-2-22-2-2-2-22222-2-22-2-2220000000000000000-222-20000000000-22200-200000000
χ432222-2-22-2-22-2-2-2-2222-222-2-2-22200000000000000002-2-2200000000000002-20-22000000
χ442222-2-22-2-22-2-2-2-2222-222-2-2-22200000000000000002-2-220000000000000-2202-2000000
χ454444-4-4-244-22222-2-2-44-44-4-2-2220000000000000000-22-22000000000000000000000000
χ464444-4-4-244-22222-2-2-4-44-44-2-22200000000000000002-22-2000000000000000000000000
χ474444-4-4-2-4-4-22222-2-244-4-4422-2-200000000000000002-2-22000000000000000000000000
χ484444-4-4-2-4-4-22222-2-24-444-422-2-20000000000000000-222-2000000000000000000000000
χ4944-4-40044-440000-4-4000004-40000002-22-22-22-22-22-20000000000000000000000000000
χ5044-4-40044-440000-4-4000004-4000000-22-22-22-22-22-220000000000000000000000000000
χ5144-4-4004-4440000-4-400000-440000002-2-222-22-2-22-220000000000000000000000000000
χ5244-4-4004-4440000-4-400000-44000000-222-2-22-222-22-20000000000000000000000000000
χ5344-4-400-24-4-2−2i3−2i32i32i32200000-22−2i32i300002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ5444-4-400-24-4-2−2i3−2i32i32i32200000-22−2i32i30000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ5544-4-400-24-4-22i32i3−2i3−2i32200000-222i3−2i300002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ5644-4-400-24-4-22i32i3−2i3−2i32200000-222i3−2i30000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ5744-4-400-2-44-2−2i3−2i32i32i322000002-22i3−2i300002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ5844-4-400-2-44-2−2i3−2i32i32i322000002-22i3−2i30000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ5944-4-400-2-44-22i32i3−2i3−2i322000002-2−2i32i300002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ6044-4-400-2-44-22i32i3−2i3−2i322000002-2−2i32i30000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ614-44-44-4400-44-44-4-440000000000000000000000000000000000000000000000000−2i22i200
χ624-44-44-4400-44-44-4-4400000000000000000000000000000000000000000000000002i2−2i200
χ634-44-4-44400-4-44-44-4400000000000000000000000000000000000000000000000−2i22i20000
χ644-44-4-44400-4-44-44-44000000000000000000000000000000000000000000000002i2−2i20000
χ658-88-88-8-4004-44-444-400000000000000000000000000000000000000000000000000000
χ668-88-8-88-40044-44-44-400000000000000000000000000000000000000000000000000000
χ678-8-8800800-800008-800000000000000000000000000000000000000000000000000000
χ688-8-8800-4004−4i34i34i3−4i3-4400000000000000000000000000000000000000000000000000000
χ698-8-8800-40044i3−4i3−4i34i3-4400000000000000000000000000000000000000000000000000000

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