Finite Group Databasebeta

← Group #10831701

Character table — Group #10831701

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424242222444444412121212121212122244488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1111111-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-1-1-11
χ5111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1111-1-1-1-1-1
χ6111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111
χ7111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ911111111111111111111-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1111-1-1111
χ1111111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-11-1-111-1-11
χ1211111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11111-111-1-111-1
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11111111-1-1-1
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-111-1
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-111-1-1-11111-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-20000000000-2-22200000000000022-2-2-2-20000000000020000000
χ18222222222-2-2-2-2222222222-2-2-2-2-20000000000-2-222000000000000-2-2222200000000000-20000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000000022-2-200000000000022-2-22200000000000-20000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000000022-2-2000000000000-2-222-2-20000000000020000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-22222-2-2-2-2-1-1-1-1111111110000000000-21111-1-1-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-22222-2-222-2-21111-1-1-1-111110000000000-211-1-1-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-222-2-22211111111-1-1-1-10000000000-211-1-111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-22211111111-1-1-1-100000000002-1-111-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-1111100000000002-1-11111-1-10000000000
χ292222-2-2-2-2222-2-222-22-2-2-2002-22-200000002-200000022-2-2000022-2-20000000000000002-200000000
χ302222-2-2-2-2222-2-222-22-2-2-2002-22-200000002-200000022-2-20000-2-222000000000000000-2200000000
χ312222-2-2-2-2222-2-222-22-2-2-2002-22-20000000-22000000-2-222000022-2-2000000000000000-2200000000
χ322222-2-2-2-2222-2-222-22-2-2-2002-22-20000000-22000000-2-2220000-2-2220000000000000002-200000000
χ332-2-2222-2-22-22-22-2-2222-2-200-2-22202i−2i000000000000000000002-22-20000000002i−2i0000000002i−2i000
χ342-2-2222-2-22-22-22-2-2222-2-200-2-22202i−2i00000000000000000000-22-220000000002i−2i000000000−2i2i000
χ352-2-2222-2-22-22-22-2-2222-2-200-2-2220−2i2i000000000000000000002-22-2000000000−2i2i000000000−2i2i000
χ362-2-2222-2-22-22-22-2-2222-2-200-2-2220−2i2i00000000000000000000-22-22000000000−2i2i0000000002i−2i000
χ372-2-22-2-22222-2-22-2-2-22-222002-2-22000002-2000000000000000000002-22-20000000002-20002-200000
χ382-2-22-2-22222-2-22-2-2-22-222002-2-22000002-200000000000000000000-22-220000000002-2000-2200000
χ392-2-22-2-22222-2-22-2-2-22-222002-2-2200000-22000000000000000000002-22-2000000000-22000-2200000
χ402-2-22-2-22222-2-22-2-2-22-222002-2-2200000-2200000000000000000000-22-22000000000-220002-200000
χ412-2-22-2-2222-222-2-2-2-22-22200-222-20002-20000000000000000002-2-222-2-2200000002-2000000000000
χ422-2-22-2-2222-222-2-2-2-22-22200-222-20002-2000000000000000000-222-2-222-200000002-2000000000000
χ432-2-22-2-2222-222-2-2-2-22-22200-222-2000-220000000000000000002-2-22-222-20000000-22000000000000
χ442-2-22-2-2222-222-2-2-2-22-22200-222-2000-22000000000000000000-222-22-2-220000000-22000000000000
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
χ474444-4-4-4-44-4-44444-44-4-4-400-44-440000000000000000000000000000000000000000000000000000
χ484444-4-4-4-4-244-4-4-2-22-222200-22-2200000004-4000000-2-222000000000000000000000000000000000
χ494444-4-4-4-4-244-4-4-2-22-222200-22-220000000-4400000022-2-2000000000000000000000000000000000
χ504444-4-4-4-4-2-4-444-2-22-2222002-22-20000000000000000000−2i3−2i32i32i300000000000000000000000000000
χ514444-4-4-4-4-2-4-444-2-22-2222002-22-200000000000000000002i32i3−2i3−2i300000000000000000000000000000
χ5244-4-44-44-4400004-4-4-444-4000000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000000000
χ5344-4-44-44-4400004-4-4-444-40000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000
χ5444-4-44-44-4-20000-2222-2-22000000000000000−2i22i2−2i32i3006−66−6i2−i2i2−i200000000000000000000000000000
χ5544-4-44-44-4-20000-2222-2-22000000000000000−2i22i22i3−2i300−66−66i2−i2i2−i200000000000000000000000000000
χ5644-4-44-44-4-20000-2222-2-220000000000000002i2−2i2−2i32i300−66−66−i2i2−i2i200000000000000000000000000000
χ5744-4-44-44-4-20000-2222-2-220000000000000002i2−2i22i3−2i3006−66−6−i2i2−i2i200000000000000000000000000000
χ5844-4-4-44-44400004-44-4-4-444-4000000000000000004-40000000000000000000000000000000000000
χ5944-4-4-44-44400004-44-4-4-44-4400000000000000000-440000000000000000000000000000000000000
χ6044-4-4-44-44-20000-22-2222-24-400000000000000000-226−6−666−6−6600000000000000000000000000000
χ6144-4-4-44-44-20000-22-2222-24-400000000000000000-22−666−6−666−600000000000000000000000000000
χ6244-4-4-44-44-20000-22-2222-2-44000000000000000002-26−6−66−666−600000000000000000000000000000
χ6344-4-4-44-44-20000-22-2222-2-44000000000000000002-2−666−66−6−6600000000000000000000000000000
χ644-44-44-4-4440000-44-4-44-4400000000000000000000000000000000000004-40000000000000000000
χ654-44-44-4-4440000-44-4-44-440000000000000000000000000000000000000-440000000000000000000
χ664-44-4-444-440000-444-4-44-40000000000000000000000000000000000000000000000000000000−2i22i20
χ674-44-4-444-440000-444-4-44-400000000000000000000000000000000000000000000000000000002i2−2i20
χ684-4-4444-4-444-44-4-4-4444-4-40044-4-40000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-24-44-422-2-2-22200-2-2220000000000000000000000000000000000−2i32i30000000000000000
χ704-4-4444-4-4-24-44-422-2-2-22200-2-22200000000000000000000000000000000002i3−2i30000000000000000
χ714-4-4444-4-4-2-44-4422-2-2-2220022-2-204i−4i000000000000000000000000000000000−2i2i00000000000000
χ724-4-4444-4-4-2-44-4422-2-2-2220022-2-20−4i4i0000000000000000000000000000000002i−2i00000000000000
χ734-4-44-4-444-24-4-44222-22-2-200-222-2000004-4000000000000000000000000000000000-220000000000
χ744-4-44-4-444-24-4-44222-22-2-200-222-200000-440000000000000000000000000000000002-20000000000
χ754-4-44-4-444-2-444-4222-22-2-2002-2-220004-4000000000000000000000000000000000-22000000000000
χ764-4-44-4-444-2-444-4222-22-2-2002-2-22000-440000000000000000000000000000000002-2000000000000
χ778-88-88-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000
χ788-88-8-888-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000

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