Finite Group Databasebeta

← Group #10853183

Character table — Group #10853183

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424242244444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-11
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-1-1111111-1
χ5111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-11-1-111-1-1-1-1-1
χ6111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111
χ7111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-11111-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-111-1-111-1-1-111-1-111-1-1-1
χ1011111111111111111111-1-11111-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-11-1-111-1-1111
χ1111111111111111111111-1-11111-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1
χ1211111111111111111111-1-11111-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-11-1-1-1-111-1-11
χ1311111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1111
χ1411111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-111-1-111-1-1-11111-1-11
χ1611111111111111111111-1-11111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-111111-1-1-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-20000000000-2-2220000000022-2-2000022000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-20000000000-2-22200000000-2-2220000-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000000022-2-20000000022-2-20000-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000000022-2-200000000-2-222000022000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-111111111000000000021111-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-22222-2-2-2-2-1-1-1-1111111110000000000-2-1-1-1-111110000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-22222-2-2-2-2221111-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-22222-2-211111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-222-2-211111111-1-1-1-100000000002-1-11111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-222-2-2221111-1-1-1-111110000000000211-1-111-1-10000000000
χ2922-22-22-2-2222-2-22-22-22-2-20022-2-20002-20000000000000000002-22-222-2-20002-20000000000000000
χ3022-22-22-2-2222-2-22-22-22-2-20022-2-20002-2000000000000000000-22-22-2-2220002-20000000000000000
χ3122-22-22-2-2222-2-22-22-22-2-20022-2-2000-220000000000000000002-22-2-2-222000-220000000000000000
χ3222-22-22-2-2222-2-22-22-22-2-20022-2-2000-22000000000000000000-22-2222-2-2000-220000000000000000
χ3322-22-22-2-22-2-2222-22-22-2-200-2-222000002i−2i00000000000000002-2-220000000002i−2i00000002i−2i00000
χ3422-22-22-2-22-2-2222-22-22-2-200-2-222000002i−2i0000000000000000-222-20000000002i−2i0000000−2i2i00000
χ3522-22-22-2-22-2-2222-22-22-2-200-2-22200000−2i2i00000000000000002-2-22000000000−2i2i0000000−2i2i00000
χ3622-22-22-2-22-2-2222-22-22-2-200-2-22200000−2i2i0000000000000000-222-2000000000−2i2i00000002i−2i00000
χ372-222-2-22-222-2-22-2-222-22-2002-22-202i−2i0000000000000000000000002i−2i2i−2i00000002i−2i00000002-2000
χ382-222-2-22-222-2-22-2-222-22-2002-22-202i−2i000000000000000000000000−2i2i−2i2i00000002i−2i0000000-22000
χ392-222-2-22-222-2-22-2-222-22-2002-22-20−2i2i0000000000000000000000002i−2i2i−2i0000000−2i2i0000000-22000
χ402-222-2-22-222-2-22-2-222-22-2002-22-20−2i2i000000000000000000000000−2i2i−2i2i0000000−2i2i00000002-2000
χ412-2-222-2-2222-22-2-222-2-2-22002-2-220000000002i−2i00002i2i−2i−2i000000002i−2i−2i2i0000000000002-20000000
χ422-2-222-2-2222-22-2-222-2-2-22002-2-220000000002i−2i00002i2i−2i−2i00000000−2i2i2i−2i000000000000-220000000
χ432-2-222-2-2222-22-2-222-2-2-22002-2-22000000000−2i2i0000−2i−2i2i2i000000002i−2i−2i2i000000000000-220000000
χ442-2-222-2-2222-22-2-222-2-2-22002-2-22000000000−2i2i0000−2i−2i2i2i00000000−2i2i2i−2i0000000000002-20000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222-4000000000022-2-20000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4222240000000000-2-2220000000000000000000000000000000000000
χ47444-4-4-4-444000044-44-4-4-4000000000000022−2200000000002222−22−2200000000000000000000000000000
χ48444-4-4-4-444000044-44-4-4-40000000000000−22220000000000−22−22222200000000000000000000000000000
χ49444-4-4-4-44-20000-2-22-2222000000000000022−2200−2i32i300i6−i6i6−i6−2−22200000000000000000000000000000
χ50444-4-4-4-44-20000-2-22-2222000000000000022−22002i3−2i300−i6i6−i6i6−2−22200000000000000000000000000000
χ51444-4-4-4-44-20000-2-22-22220000000000000−222200−2i32i300−i6i6−i6i622−2−200000000000000000000000000000
χ52444-4-4-4-44-20000-2-22-22220000000000000−2222002i3−2i300i6−i6i6−i622−2−200000000000000000000000000000
χ5344-44-44-4-4-244-4-4-22-22-22200-2-2220004-400000000000000000000000000000-220000000000000000
χ5444-44-44-4-4-244-4-4-22-22-22200-2-222000-44000000000000000000000000000002-20000000000000000
χ5544-44-44-4-4-2-4-444-22-22-2220022-2-2000004i−4i00000000000000000000000000000−2i2i00000000000000
χ5644-44-44-4-4-2-4-444-22-22-2220022-2-200000−4i4i000000000000000000000000000002i−2i00000000000000
χ5744-4-44-44-4400004-4-4-4-4440000000000000000000000000000000000000000000000000000000−2i22i20
χ5844-4-44-44-4400004-4-4-4-44400000000000000000000000000000000000000000000000000000002i2−2i20
χ594-444-4-44-44-444-4-4-444-44-400-44-440000000000000000000000000000000000000000000000000000
χ604-444-4-44-4-24-4-4422-2-22-2200-22-2204i−4i00000000000000000000000000000000000−2i2i000000000000
χ614-444-4-44-4-24-4-4422-2-22-2200-22-220−4i4i000000000000000000000000000000000002i−2i000000000000
χ624-444-4-44-4-2-444-422-2-22-22002-22-2000000000000000000000000000000000000000023−230000000000
χ634-444-4-44-4-2-444-422-2-22-22002-22-20000000000000000000000000000000000000000−23230000000000
χ644-44-444-4-440000-4-4-444-4400000000000000000000000000000000000004i−4i0000000000000000000
χ654-44-444-4-440000-4-4-444-440000000000000000000000000000000000000−4i4i0000000000000000000
χ664-4-444-4-444-44-44-444-4-4-4400-444-40000000000000000000000000000000000000000000000000000
χ674-4-444-4-44-24-44-42-2-2222-200-222-20000000004i−4i0000−2i−2i2i2i000000000000000000000000000000000
χ684-4-444-4-44-24-44-42-2-2222-200-222-2000000000−4i4i00002i2i−2i−2i000000000000000000000000000000000
χ694-4-444-4-44-2-44-442-2-2222-2002-2-22000000000000000000023−2323−2300000000000000000000000000000
χ704-4-444-4-44-2-44-442-2-2222-2002-2-220000000000000000000−2323−232300000000000000000000000000000
χ714-4-4-4-444440000-44-4-444-44-4000000000000000004-40000000000000000000000000000000000000
χ724-4-4-4-444440000-44-4-444-4-4400000000000000000-440000000000000000000000000000000000000
χ734-4-4-4-4444-200002-222-2-224-400000000000000000-226−6−666−6−6600000000000000000000000000000
χ744-4-4-4-4444-200002-222-2-224-400000000000000000-22−666−6−666−600000000000000000000000000000
χ754-4-4-4-4444-200002-222-2-22-44000000000000000002-26−6−66−666−600000000000000000000000000000
χ764-4-4-4-4444-200002-222-2-22-44000000000000000002-2−666−66−6−6600000000000000000000000000000
χ7788-8-88-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000
χ788-88-888-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000

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