Finite Group Databasebeta

← Group #10855120

Character table — Group #10855120

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424242244444444412121212121212122444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111
χ5111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11
χ6111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1-11111-1
χ7111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1111111-1-1-1
χ1011111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-111-1-11-1-1-1-1-1-1111
χ1111111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11111-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11111-1-11-1-11111-1-1-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-111-1-1-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-111111-1-111-1-11
χ1511111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-20000000022-2-2-2-200000000000002000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-200000000-2-222220000000000000-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-2220000000022-2-2220000000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-22200000000-2-222-2-200000000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-21111-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-22222-2-21111-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-2-2-22211111111-1-1-1-10000000000211-1-1-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-22222-2-22211111111-1-1-1-10000000000-2-1-11111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-111110000000000211-1-111-1-10000000000
χ2922-2-2-222-22-2-222222-2-2-2-2002-22-20000000002-20000000022-2-20000002i2i−2i−2i0000000000002i−2i00000
χ3022-2-2-222-22-2-222222-2-2-2-2002-22-20000000002-20000000022-2-2000000−2i−2i2i2i000000000000−2i2i00000
χ3122-2-2-222-22-2-222222-2-2-2-2002-22-2000000000-2200000000-2-2220000002i2i−2i−2i000000000000−2i2i00000
χ3222-2-2-222-22-2-222222-2-2-2-2002-22-2000000000-2200000000-2-222000000−2i−2i2i2i0000000000002i−2i00000
χ332-222-2-22-222-2-22-2-222-22-200-222-20002i−2i0000000000000000002-22-2002i−2i2i−2i00000002i−2i0000000000
χ342-222-2-22-222-2-22-2-222-22-200-222-20002i−2i000000000000000000-22-2200−2i2i−2i2i00000002i−2i0000000000
χ352-222-2-22-222-2-22-2-222-22-200-222-2000−2i2i0000000000000000002-22-200−2i2i−2i2i0000000−2i2i0000000000
χ362-222-2-22-222-2-22-2-222-22-200-222-2000−2i2i000000000000000000-22-22002i−2i2i−2i0000000−2i2i0000000000
χ372-222-2-22-22-222-2-2-222-22-2002-2-2202i−2i000000000000000000002-2-22000000000002i−2i0002i−2i0000000
χ382-222-2-22-22-222-2-2-222-22-2002-2-2202i−2i00000000000000000000-222-2000000000002i−2i000−2i2i0000000
χ392-222-2-22-22-222-2-2-222-22-2002-2-220−2i2i000000000000000000002-2-2200000000000−2i2i000−2i2i0000000
χ402-222-2-22-22-222-2-2-222-22-2002-2-220−2i2i00000000000000000000-222-200000000000−2i2i0002i−2i0000000
χ412-2-2-22-2222-22-22-2-22-22-2200-2-222000002-200000000000000000000002-2-2202-200000000000002-20
χ422-2-2-22-2222-22-22-2-22-22-2200-2-222000002-20000000000000000000000-222-202-20000000000000-220
χ432-2-2-22-2222-22-22-2-22-22-2200-2-22200000-2200000000000000000000002-2-220-220000000000000-220
χ442-2-2-22-2222-22-22-2-22-22-2200-2-22200000-220000000000000000000000-222-20-2200000000000002-20
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222-40000000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422224000000000022-2-20000000000000000000000000000000000000
χ47444-44-4-4-4400004-4-44-4-444-40000000000000004-4000000000000000000000000000000000000000
χ48444-44-4-4-4400004-4-44-4-44-44000000000000000-44000000000000000000000000000000000000000
χ49444-44-4-4-4-20000-222-222-24-4000000000000000-220066−6−66−66−600000000000000000000000000000
χ50444-44-4-4-4-20000-222-222-24-4000000000000000-2200−6−666−66−6600000000000000000000000000000
χ51444-44-4-4-4-20000-222-222-2-440000000000000002-20066−6−6−66−6600000000000000000000000000000
χ52444-44-4-4-4-20000-222-222-2-440000000000000002-200−6−6666−66−600000000000000000000000000000
χ5344-44-4-4-44400004-4-4-444-40000000000000−2i22i2000000−2i22i2−2i22i2000000000000000000000000000000000
χ5444-44-4-4-44400004-4-4-444-400000000000002i2−2i20000002i2−2i22i2−2i2000000000000000000000000000000000
χ5544-44-4-4-44-20000-2222-2-220000000000000−2i22i20000−2i32i3i2−i2i2−i26−6−6600000000000000000000000000000
χ5644-44-4-4-44-20000-2222-2-220000000000000−2i22i200002i3−2i3i2−i2i2−i2−666−600000000000000000000000000000
χ5744-44-4-4-44-20000-2222-2-2200000000000002i2−2i20000−2i32i3−i2i2−i2i2−666−600000000000000000000000000000
χ5844-44-4-4-44-20000-2222-2-2200000000000002i2−2i200002i3−2i3−i2i2−i2i26−6−6600000000000000000000000000000
χ5944-4-4-444-4444-4-4444-4-4-4-400-44-440000000000000000000000000000000000000000000000000000
χ6044-4-4-444-4-244-4-4-2-2-22222002-22-2000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ6144-4-4-444-4-244-4-4-2-2-22222002-22-20000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ6244-4-4-444-4-2-4-444-2-2-2222200-22-220000000004-400000000-2-22200000000000000000000000000000
χ6344-4-4-444-4-2-4-444-2-2-2222200-22-22000000000-440000000022-2-200000000000000000000000000000
χ644-444-4-44-4-24-4-4422-2-22-22002-2-220004i−4i00000000000000000000000000000000000−2i2i0000000000
χ654-444-4-44-4-24-4-4422-2-22-22002-2-22000−4i4i000000000000000000000000000000000002i−2i0000000000
χ664-444-4-44-4-2-444-422-2-22-2200-222-204i−4i00000000000000000000000000000000000−2i2i000000000000
χ674-444-4-44-4-2-444-422-2-22-2200-222-20−4i4i000000000000000000000000000000000002i−2i000000000000
χ684-44-4-44-4440000-44-444-4-40000000000000000000000000000000004i−4i00000000000000000000000
χ694-44-4-44-4440000-44-444-4-4000000000000000000000000000000000−4i4i00000000000000000000000
χ704-4-4444-4-440000-44-4-4-44400000000000000000000000000000000000000000000000000000−2i22i2000
χ714-4-4444-4-440000-44-4-4-444000000000000000000000000000000000000000000000000000002i2−2i2000
χ724-4-4-44-44444-44-4-4-44-44-440044-4-40000000000000000000000000000000000000000000000000000
χ734-4-4-44-444-24-44-422-22-22-200-2-22200000000000000000000000000000000000023−2300000000000000
χ744-4-4-44-444-24-44-422-22-22-200-2-222000000000000000000000000000000000000−232300000000000000
χ754-4-4-44-444-2-44-4422-22-22-20022-2-2000004-4000000000000000000000000000-220000000000000000
χ764-4-4-44-444-2-44-4422-22-22-20022-2-200000-440000000000000000000000000002-20000000000000000
χ778-88-8-88-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000
χ788-8-8888-8-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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