Finite Group Databasebeta

← Group #10778192

Character table — Group #10778192

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444444466668888888888888888881212121216161616161624242424242424242432324848
order1222344446664444488121212122424242444448888888121212121224242424242424884424242424248888888121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-1111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111
χ511111111111111111-1-11111-1-1-1-11111-1-1-111-1-111111-1-1-1-1-1-111-1-11-111-1-11111-1-1-1-1-11-1-11
χ611111111111111111-1-11111-1-1-1-11111-1-1-1-1-11111111-1-1-1-1-1-111-1-1-11-1-11111-1-1-1-1-111-111-1
χ711111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1111111-11-1
χ811111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-11-1-111-1-111111-1-1-11-11
χ91111111111111-1-1-1-1111111111111111-1-111111-1-1-1-111-1-1-1-11111-1-11111-1-1111-1-111-1-1-1-1
χ101111111111111-1-1-1-1111111111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-11111
χ111111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111
χ121111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1111111-1-1
χ131111111111111-1-1-1-1-1-11111-1-1-1-11111-11111-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-111-1-1-111-1
χ141111111111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-1-1-1111111-1-11-1-1-111-1-1-1-1-111111-1-11
χ151111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-1-111-1111-1-111-1-11-1-111-11-11
χ161111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1111-1-1-11111111-1-1-1-11-11-1
χ17222222-22-2222-222-2-2002-2-22000022-2-20000000-222-2-2000000-22000000002-200000000000
χ18222222-22-2222-222-2-2002-2-220000-2-2220000000-222-2-20000002-200000000-2200000000000
χ19222222-22-2222-2-2-222002-2-22000022-2-20000000-2-2-222000000-2200000000-2200000000000
χ20222222-22-2222-2-2-222002-2-220000-2-2220000000-2-2-2220000002-2000000002-200000000000
χ2122222-22-22222-2000022-222-222222222-2000000-20000-2-20000-2-2220000000000-200000000
χ2222222-22-22222-2000022-222-22222-2-2-2-2-2000000-20000-2-2000022-2-20000000000200000000
χ2322222-22-22222-20000-2-2-222-2-2-2-2-222222000000-20000220000-2-2-2-20000000000200000000
χ2422222-22-22222-20000-2-2-222-2-2-2-2-2-2-2-2-22000000-2000022000022220000000000-200000000
χ2522222-2-2-2-22222000000-2-2-2-2000022-2-202i−2i000020000002i2i−2i−2i2-200000000000002i−2i000000
χ2622222-2-2-2-22222000000-2-2-2-2000022-2-20−2i2i00002000000−2i−2i2i2i2-20000000000000−2i2i000000
χ2722222-2-2-2-22222000000-2-2-2-20000-2-22202i−2i000020000002i2i−2i−2i-220000000000000−2i2i000000
χ2822222-2-2-2-22222000000-2-2-2-20000-2-2220−2i2i00002000000−2i−2i2i2i-2200000000000002i−2i000000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000-1-100
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-10000-2-211110000000001100
χ312222-12222-1-1-122222-2-2-1-1-1-111110000-2-2-222-2-2-1-1-1-1-111111100002-2-1-111000000000-1100
χ322222-12222-1-1-122222-2-2-1-1-1-111110000-2-2-2-2-222-1-1-1-1-11111110000-2211-1-10000000001-100
χ332222-12222-1-1-12-2-2-2-222-1-1-1-1-1-1-1-100002-2-22222-11111-1-111110000-2-2-1-1-1-10000000001100
χ342222-12222-1-1-12-2-2-2-222-1-1-1-1-1-1-1-100002-2-2-2-2-2-2-11111-1-111110000221111000000000-1-100
χ352222-12222-1-1-12-2-2-2-2-2-2-1-1-1-111110000-22222-2-2-1111111-1-1-1-10000-22-1-1110000000001-100
χ362222-12222-1-1-12-2-2-2-2-2-2-1-1-1-111110000-222-2-222-1111111-1-1-1-100002-211-1-1000000000-1100
χ372-2-2220-2022-2-2000002-202-2022-2-22i−2i2i−2i0002−22−200000000000002i−2i002−22−200−i2i2000−i2i20000
χ382-2-2220-2022-2-2000002-202-2022-2-22i−2i2i−2i000−22−2200000000000002i−2i00−22−2200i2−i2000i2−i20000
χ392-2-2220-2022-2-2000002-202-2022-2-2−2i2i−2i2i0002−22−20000000000000−2i2i002−22−200i2−i2000i2−i20000
χ402-2-2220-2022-2-2000002-202-2022-2-2−2i2i−2i2i000−22−220000000000000−2i2i00−22−2200−i2i2000−i2i20000
χ412-2-2220-2022-2-200000-2202-20-2-2222i−2i2i−2i0002−2−220000000000000−2i2i002−2−2200−i2i2000i2−i20000
χ422-2-2220-2022-2-200000-2202-20-2-2222i−2i2i−2i000−222−20000000000000−2i2i00−222−200i2−i2000−i2i20000
χ432-2-2220-2022-2-200000-2202-20-2-222−2i2i−2i2i0002−2−2200000000000002i−2i002−2−2200i2−i2000−i2i20000
χ442-2-2220-2022-2-200000-2202-20-2-222−2i2i−2i2i000−222−200000000000002i−2i00−222−200−i2i2000i2−i20000
χ454444-24-44-4-2-2-2-444-4-400-222-20000000000000002-2-22200000000000000000000000000000
χ464444-24-44-4-2-2-2-4-4-44400-222-2000000000000000222-2-200000000000000000000000000000
χ474444-2-44-44-2-2-2-40000442-2-22-2-2-2-20000-40000002000022000000000000000000000000000
χ484444-2-44-44-2-2-2-40000-4-42-2-2222220000400000020000-2-2000000000000000000000000000
χ494444-2-4-4-4-4-2-2-2400000022220000000004i−4i0000-2000000−2i−2i2i2i00000000000000000000000
χ504444-2-4-4-4-4-2-2-240000002222000000000−4i4i0000-20000002i2i−2i−2i00000000000000000000000
χ514-44-4440-40-4-4404i−4i0000400-400000000000000004i−4i0000000000000000000000000000000
χ524-44-4440-40-4-440−4i4i0000400-40000000000000000−4i4i0000000000000000000000000000000
χ534-44-44-4040-4-440004-400-40040000000000000000004-400000000000000000000000000000
χ544-44-44-4040-4-44000-4400-4004000000000000000000-4400000000000000000000000000000
χ554-44-4-240-4022-204i−4i0000-2002i6−i6i6−i6000000000000−2i2i00i6−i66−66−600000000000000000000000
χ564-44-4-240-4022-204i−4i0000-2002−i6i6−i6i6000000000000−2i2i00−i6i6−66−6600000000000000000000000
χ574-44-4-240-4022-20−4i4i0000-2002i6−i6i6−i60000000000002i−2i00i6−i6−66−6600000000000000000000000
χ584-44-4-240-4022-20−4i4i0000-2002−i6i6−i6i60000000000002i−2i00−i6i66−66−600000000000000000000000
χ594-44-4-2-404022-20004-400200-2i6−i6i6−i600000000000000-22−i6i6i6−i6−i6i600000000000000000000000
χ604-44-4-2-404022-20004-400200-2−i6i6−i6i600000000000000-22i6−i6−i6i6i6−i600000000000000000000000
χ614-44-4-2-404022-2000-4400200-2i6−i6i6−i6000000000000002-2−i6i6−i6i6i6−i600000000000000000000000
χ624-44-4-2-404022-2000-4400200-2−i6i6−i6i6000000000000002-2i6−i6i6−i6−i6i600000000000000000000000
χ634-4-444040-44-4-400000000-44000004i−4i−4i4i00000000000000000000000000000000000000000
χ644-4-444040-44-4-400000000-4400000−4i4i4i−4i00000000000000000000000000000000000000000
χ654-4-44-20-404-222000004-40-220-2-222000000022−2222−2200000000000000000−22−220000000000000
χ664-4-44-20-404-222000004-40-220-2-2220000000−2222−2222000000000000000002−22−20000000000000
χ674-4-44-20-404-22200000-440-22022-2-2000000022−22−222200000000000000000−222−20000000000000
χ684-4-44-20-404-22200000-440-22022-2-20000000−222222−22000000000000000002−2−220000000000000
χ6988-8-880000-88-8000000000000000000000000000000000000000000000000000000000000
χ7088-8-8-400004-44000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ7188-8-8-400004-4400000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000
χ728-8-88-4080-8-444000000004-400000000000000000000000000000000000000000000000000

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