Finite Group Databasebeta

← Group #10772492

Character table — Group #10772492

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order12223444466622488881212121222444444444668812121224242424444888848121212122424242422444881228
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-1-1-11111-1-1111111111111-1-1-11-1-111-1-11-1-1-1-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-11-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-111
χ5111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-11-1-1-111-1-1-1-11-1-1-1-1111-1-1-1-111-11-1-1-1-1111-1-1-1-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-11111111-1-1111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-1-111-1-1-1-11-1-1-1-1-1-1-1111111-11-1-1-1-111-11111111-1-1
χ9111111111111-1-11111111111111111-11-1-1-1-1-1-11111111-1-111111-111-1-1-1-1-111-111-1-1-1-1-1-11
χ10111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-111111-1-1111111-1-1-111-1-1-1-1-1-1-111-1-111-1
χ11111111111111-1-1111111111-1-1-1-1-1-11-11-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1111-1-11111-11-1
χ12111111111111-1-1111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1-11-1-1-111-1-1-1-1111-1-1111-11
χ13111111111111-1-11-1-1-1-111111111111-11-1-1-1-111111-1-1-1-1-1-11-1-1-1-11-11-1-1-111-1-1-111-1-11111-1
χ14111111111111-1-11-1-1-1-11111111111-1-1-111-1-111-1-11-1-1-1-1-1-11-1-1-1-1-11-1-1111111-1-1-11111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-111111-1-1-1-111-111111-11-1-1-111-1-11-1-111-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-111-11111-11-1-1111111111-1-1-1-1-11-1
χ17222222-2-2222200-20000-22-2222-2-22220-2000000-2-2-2000000-20000002000000002-20000000
χ18222222-2-2222200-20000-22-2222-2-222-20200000022-2000000-2000000-200000000-220000000
χ19222222-2-2222200-20000-22-22-2-222-2-220-2000000-2-2-20000002000000200000000-220000000
χ20222222-2-2222200-20000-22-22-2-222-2-2-20200000022-20000002000000-2000000002-20000000
χ2122222-222-222222-200002-22-222-2-2-2-20-2000220000-20000-2-220000000-20000002000000000
χ2222222-222-222222-200002-22-2-2-222220-2000220000-2000022-20000000-2000000-2000000000
χ2322222-222-2222-2-2-200002-22-222-2-2-2-202000-2-20000-2000022200000002000000-2000000000
χ2422222-222-2222-2-2-200002-22-2-2-2222202000-2-20000-20000-2-2-2000000020000002000000000
χ2522222-2-2-2-22220020000-2-2-2-22222-2-20002-20000002000000-2000000002-200000002-200000
χ2622222-2-2-2-22220020000-2-2-2-22222-2-2000-220000002000000-200000000-220000000-2200000
χ2722222-2-2-2-22220020000-2-2-2-2-2-2-2-2220002-200000020000002000000002-20000000-2200000
χ2822222-2-2-2-22220020000-2-2-2-2-2-2-2-222000-220000002000000200000000-2200000002-200000
χ292222-12222-1-1-12222222-1-1-1-100000022222-1-122-1-1-1-1-1-1-1000000022-1-1-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-1000000-22-2-2-2-1-12211-1-1-1-1-10000000-2-21-111-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-1-1-2-2-1-1-111110000000-2-2-1-1-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-22-2-2-2-1-1-2-211-111110000000221-11111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-10000002-22-2-211-2-2-1-1-1-1-1-1-10000000-22-111111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-2-22211-2-211-1-1-1-1-100000002-211-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-10000002-22-2-21122-1-1-1111100000002-2-1111-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-2-222112211-111110000000-2211-1-1-1-1-1-10000000100
χ372-2-2220-2202-2-22-2022−2−220-20002i−2i2i−2i000002-22−200022−2−22i−2i0−i2−i2i2i20000002−20000000−i2i2000
χ382-2-2220-2202-2-22-2022−2−220-2000−2i2i−2i2i000002-22−200022−2−2−2i2i0i2i2−i2−i20000002−20000000i2−i2000
χ392-2-2220-2202-2-22-20−2−22220-20002i−2i2i−2i000002-2−22000−2−2222i−2i0i2i2−i2−i2000000−220000000i2−i2000
χ402-2-2220-2202-2-22-20−2−22220-2000−2i2i−2i2i000002-2−22000−2−222−2i2i0−i2−i2i2i2000000−220000000−i2i2000
χ412-2-2220-2202-2-2-22022−2−220-20002i−2i2i−2i00000-22−2200022−2−2−2i2i0−i2−i2i2i2000000−220000000i2−i2000
χ422-2-2220-2202-2-2-22022−2−220-2000−2i2i−2i2i00000-22−2200022−2−22i−2i0i2i2−i2−i2000000−220000000−i2i2000
χ432-2-2220-2202-2-2-220−2−22220-20002i−2i2i−2i00000-222−2000−2−222−2i2i0i2i2−i2−i20000002−20000000−i2i2000
χ442-2-2220-2202-2-2-220−2−22220-2000−2i2i−2i2i00000-222−2000−2−2222i−2i0−i2−i2i2i20000002−20000000i2−i2000
χ454444-24-4-44-2-2-200-400002-22-200000040-40000002220000000000000-200000000000000000
χ464444-24-4-44-2-2-200-400002-22-2000000-404000000-2-220000000000000200000000000000000
χ474444-2-444-4-2-2-244-40000-22-220000000-4000-2-2000020000000000000020000000000000000
χ484444-2-444-4-2-2-2-4-4-40000-22-2200000004000220000200000000000000-20000000000000000
χ494444-2-4-4-4-4-2-2-2004000022220000000004-4000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-200400002222000000000-44000000-20000000000000002-200000000000000
χ5144-4-440000-44-40002i−2i2i−2i00004-400000000000000002i−2i2i−2i0002i−2i2i−2i00000000000000000000
χ5244-4-440000-44-40002i−2i2i−2i0000-4400000000000000002i−2i2i−2i000−2i2i−2i2i00000000000000000000
χ5344-4-440000-44-4000−2i2i−2i2i00004-40000000000000000−2i2i−2i2i000−2i2i−2i2i00000000000000000000
χ5444-4-440000-44-4000−2i2i−2i2i0000-440000000000000000−2i2i−2i2i0002i−2i2i−2i00000000000000000000
χ554-44-44400-4-4-44000−2i22i22i2−2i2040-4000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ564-44-44400-4-4-440002i2−2i2−2i22i2040-40000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ574-44-44-4004-4-4400000000-404000000000000000000000000022−22−222200000000000000000000
χ584-44-44-4004-4-4400000000-4040000000000000000000000000−222222−2200000000000000000000
χ594-44-4-2400-422-2000−2i22i22i2−2i20-202000000000000000−2i32i30i2−i2−i2i20000000000000006−60000000000
χ604-44-4-2400-422-2000−2i22i22i2−2i20-2020000000000000002i3−2i30i2−i2−i2i2000000000000000−660000000000
χ614-44-4-2400-422-20002i2−2i2−2i22i20-202000000000000000−2i32i30−i2i2i2−i2000000000000000−660000000000
χ624-44-4-2400-422-20002i2−2i2−2i22i20-2020000000000000002i3−2i30−i2i2i2−i20000000000000006−60000000000
χ634-4-44404-404-4-40000000-4040004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-4-44404-404-4-40000000-404000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-4-44-20-440-2224-402222−22−22-202000000000000-2222−22000−2−2220000000000000−22000000000000
χ664-4-44-20-440-2224-40−22−222222-202000000000000-22−222200022−2−200000000000002−2000000000000
χ674-4-44-20-440-222-4402222−22−22-2020000000000002-2−2222000−2−22200000000000002−2000000000000
χ684-4-44-20-440-222-440−22−222222-2020000000000002-222−2200022−2−20000000000000−22000000000000
χ6988-8-8-400004-440004i−4i4i−4i0000000000000000000000−2i2i−2i2i000000000000000000000000000
χ7088-8-8-400004-44000−4i4i−4i4i00000000000000000000002i−2i2i−2i000000000000000000000000000
χ718-88-8-4-800844-40000000040-40000000000000000000000000000000000000000000000000
χ728-8-88-408-80-444000000040-400000000000000000000000000000000000000000000000000

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