Finite Group Databasebeta

← Group #10901356

Character table — Group #10901356

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order1222222234444666666622441212121244444444668888121224242424242424244444444412121212121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1
χ911111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-111-1-111-1-11111-1-11-1
χ1011111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1-111-1-111-11
χ1111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-111-1-1-11
χ1211111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1
χ1311111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-111-11
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-11-1-1-1-1111111-1-111-1-11-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111-11111-1-1-1-1-1-11111-1-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2-222220000220000-2-200000000-2-222-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000220000-2-20000000022-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-222220000-2-200002200000000-2-2-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-20000-2-2000022000000002222-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-100002222-1-12222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-100002222-1-1-2-2-2-2-1-111111111000000-2-2-1-11111-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-1-1-2-2-2-2-1-1111111110000002211-1-1-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-21122-2-211-1-1-1-111110000002-211-1-111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-211-2-222111111-1-1-1-1000000-221111-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2221122-2-211-1-1-1-11111000000-22-1-111-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22211-2-222111111-1-1-1-10000002-2-1-1-1-111110000000000
χ2922-2-22-22-2200002-2-222-2-22-200000022-2-200002-2−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2002-20000000000000000−i2i2−i2i200
χ3022-2-22-22-2200002-2-222-2-22-200000022-2-200002-2i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2002-20000000000000000i2−i2i2−i200
χ3122-2-22-22-2200002-2-222-2-22-2000000-2-22200002-2−i2i2−i2i200−i2−i2i2i2−i2−i2i2i200-220000000000000000i2−i2i2−i200
χ3222-2-22-22-2200002-2-222-2-22-2000000-2-22200002-2i2−i2i2−i200i2i2−i2−i2i2i2−i2−i200-220000000000000000−i2i2−i2i200
χ3322-2-22-22-2200002-2-222-2-2-2200000022-2-20000-22−i2i2i2−i200−i2−i2i2i2i2i2−i2−i200-220000000000000000−i2i2i2−i200
χ3422-2-22-22-2200002-2-222-2-2-2200000022-2-20000-22i2−i2−i2i200i2i2−i2−i2−i2−i2i2i200-220000000000000000i2−i2−i2i200
χ3522-2-22-22-2200002-2-222-2-2-22000000-2-2220000-22−i2i2i2−i200−i2−i2i2i2i2i2−i2−i2002-20000000000000000i2−i2−i2i200
χ3622-2-22-22-2200002-2-222-2-2-22000000-2-2220000-22i2−i2−i2i200i2i2−i2−i2−i2−i2i2i2002-20000000000000000−i2i2i2−i200
χ372-2-2-2-222222-22-2-2-2-22-22200002-22-22-22-2002-200000000000000002-20000002-20000002-200000000
χ382-2-2-2-222222-22-2-2-2-22-22200002-22-22-22-200-2200000000000000002-2000000-22000000-2200000000
χ392-2-2-2-222222-22-2-2-2-22-22200002-22-2-22-22002-20000000000000000-220000002-2000000-2200000000
χ402-2-2-2-222222-22-2-2-2-22-22200002-22-2-22-2200-220000000000000000-22000000-220000002-200000000
χ412-2-2-2-22222-22-22-2-2-22-2220000-22-222-22-22-2000000000000000000-220000000000002-2002-2000000
χ422-2-2-2-22222-22-22-2-2-22-2220000-22-222-22-2-22000000000000000000-22000000000000-2200-22000000
χ432-2-2-2-22222-22-22-2-2-22-2220000-22-22-22-222-20000000000000000002-20000000000002-200-22000000
χ442-2-2-2-22222-22-22-2-2-22-2220000-22-22-22-22-220000000000000000002-2000000000000-22002-2000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222200000000-2-20000220000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200000000220000-2-20000000000000000000000000000000000
χ47444-4-44-4-444-4-4444-4-4-4-4400004-4-4400000000000000000000000000000000000000000000000000
χ48444-4-44-4-44-444-444-4-4-4-440000-444-400000000000000000000000000000000000000000000000000
χ49444-4-44-4-4-24-4-44-2-22222-20000-222-2000000000000000000000000000000000023−2300000000000000
χ50444-4-44-4-4-24-4-44-2-22222-20000-222-20000000000000000000000000000000000−232300000000000000
χ51444-4-44-4-4-2-444-4-2-22222-200002-2-2200000000000000000000000000000000000023−23000000000000
χ52444-4-44-4-4-2-444-4-2-22222-200002-2-22000000000000000000000000000000000000−2323000000000000
χ5344-44-4-4-44400004-44-4-44-40000000000000000000000000000000000004-400000000000000000000
χ5444-44-4-4-44400004-44-4-44-4000000000000000000000000000000000000-4400000000000000000000
χ5544-4-44-44-4-20000-222-2-2224-400000000000000-22−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ5644-4-44-44-4-20000-222-2-2224-400000000000000-222i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ5744-4-44-44-4-20000-222-2-222-44000000000000002-2−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ5844-4-44-44-4-20000-222-2-222-44000000000000002-22i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ594-444-4-44-440000-4444-4-4-4000000004-4-440000000000000000000000000000000000000000000000
χ604-444-4-44-440000-4444-4-4-400000000-444-40000000000000000000000000000000000000000000000
χ614-44-44-4-4440000-44-4-444-4004i−4i0000000000000000004i−4i0000000000000000000000000000000000
χ624-44-44-4-4440000-44-4-444-400−4i4i000000000000000000−4i4i0000000000000000000000000000000000
χ634-44-44-4-44-200002-222-2-22004i−4i000000000000000000−2i2i6−66−6i6−i6i6−i600000000000000000000000000
χ644-44-44-4-44-200002-222-2-22004i−4i000000000000000000−2i2i−66−66−i6i6−i6i600000000000000000000000000
χ654-44-44-4-44-200002-222-2-2200−4i4i0000000000000000002i−2i6−66−6−i6i6−i6i600000000000000000000000000
χ664-44-44-4-44-200002-222-2-2200−4i4i0000000000000000002i−2i−66−66i6−i6i6−i600000000000000000000000000
χ674-4-4444-4-4444-4-4-4-44-44-44000044-4-400000000000000000000000000000000000000000000000000
χ684-4-4444-4-44-4-444-4-44-44-440000-4-44400000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-244-4-422-22-22-20000-2-2220000000000000000000023−23−232300000000000000000000000000
χ704-4-4444-4-4-244-4-422-22-22-20000-2-22200000000000000000000−232323−2300000000000000000000000000
χ714-4-4444-4-4-2-4-44422-22-22-2000022-2-20000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ724-4-4444-4-4-2-4-44422-22-22-2000022-2-200000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ734-4-4-4-4444-24-44-4222-22-2-20000-22-220000004-4000000000000000000000000-220000000000000000
χ744-4-4-4-4444-24-44-4222-22-2-20000-22-22000000-440000000000000000000000002-20000000000000000
χ754-4-4-4-4444-2-44-44222-22-2-200002-22-200004-400000000000000000000000000000000-220000000000
χ764-4-4-4-4444-2-44-44222-22-2-200002-22-20000-44000000000000000000000000000000002-20000000000
χ7788-88-8-8-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ788-888-8-88-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000

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