Finite Group Databasebeta

← Group #10770239

Character table — Group #10770239

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order12222222366624444666612121212121224446888812242424242424242424666121212121222444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-111-1-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-111-1-1-111-1-111-1-1111111-1-1
χ911111-1-111111-1-1-11111-1-1-1-1-1-1111-1-11-111-1-111111-1-1-1-11-11111-1-1-1-11-11-11-11-111-1-11-1
χ1011111-1-111111-1-1-11111-1-1-1-1-1-1111-1-11-111-1-111111-1-1-1-11-11111-1-1-1-1-11-11-11-11-1-111-11
χ1111111-1-111111-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1111-1-1-1-11111-111-1-11-1-1111-11-11-11-1-1-111-11
χ1211111-1-111111-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1111-1-1-1-11111-111-1-11-1-111-11-11-11-1111-1-11-1
χ1311111-1-111111-1-1-11111-1-1-1-1-1-111-111-1-111-1-111111-1-1-1-1-11-1-1-1-111111-1-111-1-1111-1-1-11
χ1411111-1-111111-1-1-11111-1-1-1-1-1-111-111-1-111-1-111111-1-1-1-1-11-1-1-1-11111-111-1-111-1-1-1111-1
χ1511111-1-111111-1-1-11111-1-1-1-1-1-111-111-1-1-1-1111-1-1-1-111111-1-111-111-1-11-1-111-1-11-1-1111-1
χ1611111-1-111111-1-1-11111-1-1-1-1-1-111-111-1-1-1-1111-1-1-1-111111-1-111-111-1-1-111-1-111-111-1-1-11
χ172222222222222-2-2-2-22222-2-2-2-2-2-2000020000-2000000000000000000002-200-22000000
χ182222222222222-2-2-2-22222-2-2-2-2-2-2000020000-200000000000000000000-22002-2000000
χ1922222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ2022222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111-2-2-111-1-1-11100000000000000
χ2122222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ2222222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111221-1-1111-1-100000000000000
χ2322222-2-222222-222-2-222-2-22222-2-20000-20000-2000000000000000000002200-2-2000000
χ2422222-2-222222-222-2-222-2-22222-2-20000-20000-200000000000000000000-2-20022000000
χ2522222-2-22-1-1-1-1-2-2-222-1-1111111-1-12-2-22122-2-2-1-1-1-1-111112-2-1-1-1-1111100000000000000
χ2622222-2-22-1-1-1-1-2-2-222-1-1111111-1-12-2-221-2-222-11111-1-1-1-1-22-111-111-1-100000000000000
χ2722222-2-22-1-1-1-1-2-2-222-1-1111111-1-1-222-2122-2-2-1-1-1-1-11111-221111-1-1-1-100000000000000
χ2822222-2-22-1-1-1-1-2-2-222-1-1111111-1-1-222-21-2-222-11111-1-1-1-12-21-1-11-1-11100000000000000
χ292222-222-22222-22-22-2-2-22222-2-22222-2-2-20000-20000000000200-22-20000000000000000
χ302222-222-22222-22-22-2-2-22222-2-222-2-222-20000-20000000000-2002-220000000000000000
χ312222-222-22222-2-22-22-2-222-2-222-2-20000-2000020000000000000000002200-2-200000000
χ322222-222-22222-2-22-22-2-222-2-222-2-20000-200002000000000000000000-2-2002200000000
χ332222-222-2-1-1-1-1-22-22-211-1-1-1-111-1-122-2-2100001−i3−i3i3i3−i3−i3i3i300-1−i3i31-11−i3i300000000000000
χ342222-222-2-1-1-1-1-22-22-211-1-1-1-111-1-122-2-2100001i3i3−i3−i3i3i3−i3−i300-1i3−i31-11i3−i300000000000000
χ352222-222-2-1-1-1-1-22-22-211-1-1-1-111-1-1-2-222100001−i3−i3i3i3−i3−i3i3i3001i3−i3-11-1i3−i300000000000000
χ362222-222-2-1-1-1-1-22-22-211-1-1-1-111-1-1-2-222100001i3i3−i3−i3i3i3−i3−i3001−i3i3-11-1−i3i300000000000000
χ372222-2-2-2-2222222-2-22-2-2-2-222-2-2-2-200002000020000000000000000002-200-2200000000
χ382222-2-2-2-2222222-2-22-2-2-2-222-2-2-2-20000200002000000000000000000-22002-200000000
χ392222-2-2-2-222222-222-2-2-2-2-2-2-222222-22-220000-20000000000200-2-220000000000000000
χ402222-2-2-2-222222-222-2-2-2-2-2-2-22222-22-2220000-20000000000-20022-20000000000000000
χ412222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-12-22-2-100001−i3−i3i3i3i3i3−i3−i300-1−i3i311-1i3−i300000000000000
χ422222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-12-22-2-100001i3i3−i3−i3−i3−i3i3i300-1i3−i311-1−i3i300000000000000
χ432222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-1-22-22-100001−i3−i3i3i3i3i3−i3−i3001i3−i3-1-11−i3i300000000000000
χ442222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-1-22-22-100001i3i3−i3−i3−i3−i3i3i3001−i3i3-1-11i3−i300000000000000
χ4544444444-2-2-2-24-4-4-4-4-2-2-2-22222220000-20000200000000000000000000000000000000
χ4644444-4-44-2-2-2-2-444-4-4-2-222-2-2-2-222000020000200000000000000000000000000000000
χ474444-444-4-2-2-2-2-4-44-4422-2-222-2-222000020000-200000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-244-4-442222-2-222220000-20000-200000000000000000000000000000000
χ4944-4-404-404-44-400000004-40000000000000000000000000000000000000000002i−2i2i−2i00
χ5044-4-404-404-44-400000004-4000000000000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-40-4404-44-40000000-440000000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-40-4404-44-40000000-44000000000000000000000000000000000000000000−2i2i2i−2i00
χ534-4-44400-444-4-4000004-4000000000000000−2i22i200000−2i22i2−2i22i2000000000000000000000000
χ544-4-44400-444-4-4000004-40000000000000002i2−2i2000002i2−2i22i2−2i2000000000000000000000000
χ554-4-44400-4-2-22200000-220023−2323−23000000000−2i22i20i6−i6i6−i6i2−i2i2−i2000000000000000000000000
χ564-4-44400-4-2-22200000-220023−2323−230000000002i2−2i20−i6i6−i6i6−i2i2−i2i2000000000000000000000000
χ574-4-44400-4-2-22200000-2200−2323−2323000000000−2i22i20−i6i6−i6i6i2−i2i2−i2000000000000000000000000
χ584-4-44400-4-2-22200000-2200−2323−23230000000002i2−2i20i6−i6i6−i6−i2i2−i2i2000000000000000000000000
χ594-4-44-400444-4-400000-44000000000000022−2200022−22−22220000000000000000000000000000
χ604-4-44-400444-4-400000-440000000000000−2222000−222222−220000000000000000000000000000
χ614-4-44-4004-2-222000002-20023−23−2323000000022−22000−222−26−6−66000000000000000000000000
χ624-4-44-4004-2-222000002-20023−23−23230000000−22220002−2−22−666−6000000000000000000000000
χ634-4-44-4004-2-222000002-200−232323−23000000022−22000−222−2−666−6000000000000000000000000
χ644-4-44-4004-2-222000002-200−232323−230000000−22220002−2−226−6−66000000000000000000000000
χ6588-8-808-80-44-440000000-44000000000000000000000000000000000000000000000000
χ6688-8-80-880-44-4400000004-4000000000000000000000000000000000000000000000000
χ678-88-800008-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-80000-444-40000000000000−4i34i3000000000000000000000000000000000000000000
χ698-88-80000-444-400000000000004i3−4i3000000000000000000000000000000000000000000

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