Finite Group Databasebeta

← Group #10695416

Character table — Group #10695416

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222244444444888888888888888816161616161616161616161624242424242424242424242424242424
order122222222222366666664444666644441212121212121212121212122444661212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ922222222222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1111111112-2-22-1-11111-1-10000000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-111111111-222-211-1-1-1-1110000000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000−i3i3−i3−i3i3i3−i3i30000000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000i3−i3i3i3−i3−i3i3−i30000000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3i3i3i3−i3−i3−i3i30000000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3−i3−i3−i3i3i3i3−i30000000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-2000022-2-20000000002-20002-22-2000000000000000000
χ2022222222-2-2-2-2222222222-22-2-2-2-2-2000022-2-2000000000-22000-22-22000000000000000000
χ2122222222-2-2-2-222222222-22-22-2-2-2-20000-2-22200000000200-2220000-2-20000000000000000
χ2222222222-2-2-2-222222222-22-22-2-2-2-20000-2-22200000000-2002-2-20000220000000000000000
χ2322222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000-1-111−i3−i3i3i3−i3−i3i3i302-20−i3i3-11-11i3−i30000000000000000
χ2422222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000-1-111−i3−i3i3i3−i3−i3i3i30-220i3−i31-11-1−i3i30000000000000000
χ2522222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000-1-111i3i3−i3−i3i3i3−i3−i302-20i3−i3-11-11−i3i30000000000000000
χ2622222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000-1-111i3i3−i3−i3i3i3−i3−i30-220−i3i31-11-1i3−i30000000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111000011-1-1−i3−i3i3i3i3i3−i3−i3200-2-1-1−i3i3i3−i3110000000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111000011-1-1−i3−i3i3i3i3i3−i3−i3-200211i3−i3−i3i3-1-10000000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111000011-1-1i3i3−i3−i3−i3−i3i3i3200-2-1-1i3−i3−i3i3110000000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111000011-1-1i3i3−i3−i3−i3−i3i3i3-200211−i3i3i3−i3-1-10000000000000000
χ31222-2-2-2-2222-2-2222-2-2-22-2000022-2-22i−2i0000002i−2i2i−2i00000000000000000000000022−2−2−i2−i2i2i2
χ32222-2-2-2-2222-2-2222-2-2-22-2000022-2-22i−2i0000002i−2i2i−2i000000000000000000000000−2−222i2i2−i2−i2
χ33222-2-2-2-2222-2-2222-2-2-22-2000022-2-2−2i2i000000−2i2i−2i2i00000000000000000000000022−2−2i2i2−i2−i2
χ34222-2-2-2-2222-2-2222-2-2-22-2000022-2-2−2i2i000000−2i2i−2i2i000000000000000000000000−2−222−i2−i2i2i2
χ352-2-22-2-2222-22-22-2-22-2-22222-2-22-22-200002-22-2000000000000000000000000000000002i−2i2i−2i
χ362-2-22-2-2222-22-22-2-22-2-22222-2-22-22-200002-22-200000000000000000000000000000000−2i2i−2i2i
χ372-2-22-2-2222-22-22-2-22-2-222-2-2222-22-20000-22-2200000000000000000000000000002-22-20000
χ382-2-22-2-2222-22-22-2-22-2-222-2-2222-22-20000-22-220000000000000000000000000000-22-220000
χ392-2-22-2-222-22-222-2-22-2-2222-2-22-22-2200002-2-220000000000000000000022-2-2000000000000
χ402-2-22-2-222-22-222-2-22-2-2222-2-22-22-2200002-2-2200000000000000000000-2-222000000000000
χ412-2-22-2-222-22-222-2-22-2-222-222-2-22-220000-222-200000000000000000000000022-2-200000000
χ422-2-22-2-222-22-222-2-22-2-222-222-2-22-220000-222-2000000000000000000000000-2-22200000000
χ432-2-2-222-222-2-222-2-2-2222-200002-2-22002-2000000002-22-2000000000000000000002−2−222−2−22
χ442-2-2-222-222-2-222-2-2-2222-200002-2-22002-2000000002-22-200000000000000000000−222−2−222−2
χ452-2-2-222-222-2-222-2-2-2222-200002-2-2200-2200000000-22-22000000000000000000002−2−22−222−2
χ462-2-2-222-222-2-222-2-2-2222-200002-2-2200-2200000000-22-2200000000000000000000−222−22−2−22
χ47444-4-4-4-4444-4-4-2-2-2222-220000-2-2224i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ48444-4-4-4-4444-4-4-2-2-2222-220000-2-222−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ49444-4-4-4-44-4-444444-4-4-44-40000-4-44400000000000000000000000000000000000000000000
χ50444-4-4-4-44-4-444-2-2-2222-22000022-2-20000000023−23−232300000000000000000000000000000000
χ51444-4-4-4-44-4-444-2-2-2222-22000022-2-200000000−232323−2300000000000000000000000000000000
χ5244-444-4-4-4000044-444-4-4-400000000000000000000000000000000000000002-22-200000000
χ5344-444-4-4-4000044-444-4-4-40000000000000000000000000000000000000000-22-2200000000
χ5444-4-4-444-4000044-4-4-44-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ5544-4-4-444-4000044-4-4-44-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ564-444-44-4-400004-444-44-4-400000000000000000000000000000000000000002-2-2200000000
χ574-444-44-4-400004-444-44-4-40000000000000000000000000000000000000000-222-200000000
χ584-44-44-44-400004-44-44-4-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ594-44-44-44-400004-44-44-4-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ604-4-44-4-4444-44-4-222-222-2-244-4-4-22-220000-22-22000000000000000000000000000000000000
χ614-4-44-4-4444-44-4-222-222-2-2-4-444-22-2200002-22-2000000000000000000000000000000000000
χ624-4-44-4-444-44-44-222-222-2-24-4-442-22-20000-222-2000000000000000000000000000000000000
χ634-4-44-4-444-44-44-222-222-2-2-444-42-22-200002-2-22000000000000000000000000000000000000
χ644-4-4-444-444-4-44-2222-2-2-220000-222-2004-400000000-22-220000000000000000000000000000
χ654-4-4-444-444-4-44-2222-2-2-220000-222-200-44000000002-22-20000000000000000000000000000
χ664-4-4-444-44-444-44-4-4-4444-40000-444-400000000000000000000000000000000000000000000
χ674-4-4-444-44-444-4-2222-2-2-2200002-2-22000000000000−2i32i32i3−2i30000000000000000000000000000
χ684-4-4-444-44-444-4-2222-2-2-2200002-2-220000000000002i3−2i3−2i32i30000000000000000000000000000
χ6988-888-8-8-80000-4-44-4-44440000000000000000000000000000000000000000000000000000
χ7088-8-8-888-80000-4-4444-44-40000000000000000000000000000000000000000000000000000
χ718-888-88-8-80000-44-4-44-4440000000000000000000000000000000000000000000000000000
χ728-88-88-88-80000-44-44-444-40000000000000000000000000000000000000000000000000000

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