Finite Group Databasebeta

← Group #10827372

Character table — Group #10827372

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order1222222222223444466666664466661212121222222244666666668888121224242424242424244444444488888888661212244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1111-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-11-1-1-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1111-1-1-11-1
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1111-11
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-1-11-1-11-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-1-1-11
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11111-1
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-200000000000000000000-2-20000000022220000000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-200000000000000000000-2-200000000-2-2-2-20000000000000000220000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000000000001111000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-1111111110000000000000000-1-1-1-1000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-100000000000000001111000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000000000000220000000022-2-20000000000000000-220000
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000000002200000000-2-22200000000000000002-20000
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-222-2-2-1-1-1-1111122-2-211-1-1-1-111110000000000000000-1-111000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-2-222-1-1-1-11111-2-222111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-22222-2-21111-1-1-1-1-2-222111111-1-1-1-10000000000000000-1-111000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-222-2-2221111-1-1-1-122-2-211-1-1-1-11111000000000000000011-1-1000000
χ292222-2-2-2-222-2-22000022-2-2-22-20022-2-2000000000000000000002−22−20022−2−222−2−22i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i20000000000
χ302222-2-2-2-222-2-22000022-2-2-22-20022-2-2000000000000000000002−22−20022−2−222−2−2−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i20000000000
χ312222-2-2-2-222-2-22000022-2-2-22-20022-2-200000000000000000000−22−2200−2−222−2−2222i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i20000000000
χ322222-2-2-2-222-2-22000022-2-2-22-20022-2-200000000000000000000−22−2200−2−222−2−222−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i20000000000
χ332222-2-2-2-2-2-2222000022-2-2-22-200-2-222000000000000000000002−2−220022−2−2−2−2222i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000000000
χ342222-2-2-2-2-2-2222000022-2-2-22-200-2-222000000000000000000002−2−220022−2−2−2−222−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000000000
χ352222-2-2-2-2-2-2222000022-2-2-22-200-2-22200000000000000000000−222−200−2−22222−2−22i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000
χ362222-2-2-2-2-2-2222000022-2-2-22-200-2-22200000000000000000000−222−200−2−22222−2−2−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000000000
χ3722-2-222-2-20000222-2-22-22-2-2-220000002-22-2002-20000000022-2-20000000000000000002i2i−2i−2i2i−2i2i−2i00000000000000
χ3822-2-222-2-20000222-2-22-22-2-2-220000002-22-2002-20000000022-2-2000000000000000000−2i−2i2i2i−2i2i−2i2i00000000000000
χ3922-2-222-2-20000222-2-22-22-2-2-220000002-22-200-2200000000-2-2220000000000000000002i2i−2i−2i−2i2i−2i2i00000000000000
χ4022-2-222-2-20000222-2-22-22-2-2-220000002-22-200-2200000000-2-222000000000000000000−2i−2i2i2i2i−2i2i−2i00000000000000
χ412-22-22-22-2000022-22-2-22-22-2-220000002-2-222-200000022-2-200000000000000000000002i−2i2i−2i00002i−2i2i−2i0000000000
χ422-22-22-22-2000022-22-2-22-22-2-220000002-2-222-200000022-2-20000000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000
χ432-22-22-22-2000022-22-2-22-22-2-220000002-2-22-22000000-2-22200000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000
χ442-22-22-22-2000022-22-2-22-22-2-220000002-2-22-22000000-2-2220000000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000
χ452-2-222-2-222-22-222-2-22-2-2-2-22222-22-22-222-2-2000000000000000000002-20000000000002-2-22000000000000002-200
χ462-2-222-2-222-22-222-2-22-2-2-2-22222-22-22-222-2-2000000000000000000002-2000000000000-222-200000000000000-2200
χ472-2-222-2-222-22-22-222-2-2-2-2-2222-222-22-2-2-22200002-22-2000000000000-220000000000000000000000002-22-2000000
χ482-2-222-2-222-22-22-222-2-2-2-2-2222-222-22-2-2-2220000-22-22000000000000-22000000000000000000000000-22-22000000
χ492-2-222-2-222-22-2-1-222-21111-1-1-1-22-11-1111-1-100002-22-2−i3i3−i3i3−i3i3−i3i300001-1−i3i3−i3i3−i3i3−i3i30000000000000000-11-11000000
χ502-2-222-2-222-22-2-1-222-21111-1-1-1-22-11-1111-1-100002-22-2i3−i3i3−i3i3−i3i3−i300001-1i3−i3i3−i3i3−i3i3−i30000000000000000-11-11000000
χ512-2-222-2-222-22-2-1-222-21111-1-1-1-22-11-1111-1-10000-22-22−i3i3−i3i3−i3i3−i3i300001-1i3−i3i3−i3i3−i3i3−i300000000000000001-11-1000000
χ522-2-222-2-222-22-2-1-222-21111-1-1-1-22-11-1111-1-10000-22-22i3−i3i3−i3i3−i3i3−i300001-1−i3i3−i3i3−i3i3−i3i300000000000000001-11-1000000
χ532-2-222-2-22-22-2222-2-22-2-2-2-2222-22-22-2222-2-200000000000000000000-220000000000002-2-2200000000000000-2200
χ542-2-222-2-22-22-2222-2-22-2-2-2-2222-22-22-2222-2-200000000000000000000-22000000000000-222-2000000000000002-200
χ552-2-222-2-22-22-222-222-2-2-2-2-22222-2-22-22-2-22200002-2-220000000000002-20000000000000000000000002-2-22000000
χ562-2-222-2-22-22-222-222-2-2-2-2-22222-2-22-22-2-2220000-222-20000000000002-2000000000000000000000000-222-2000000
χ572-2-222-2-22-22-22-1-222-21111-1-1-12-21-11-111-1-100002-2-22−i3i3−i3i3i3−i3i3−i30000-11−i3i3−i3i3i3−i3i3−i30000000000000000-111-1000000
χ582-2-222-2-22-22-22-1-222-21111-1-1-12-21-11-111-1-100002-2-22i3−i3i3−i3−i3i3−i3i30000-11i3−i3i3−i3−i3i3−i3i30000000000000000-111-1000000
χ592-2-222-2-22-22-22-1-222-21111-1-1-12-21-11-111-1-10000-222-2−i3i3−i3i3i3−i3i3−i30000-11i3−i3i3−i3−i3i3−i3i300000000000000001-1-11000000
χ602-2-222-2-22-22-22-1-222-21111-1-1-12-21-11-111-1-10000-222-2i3−i3i3−i3−i3i3−i3i30000-11−i3i3−i3i3i3−i3i3−i300000000000000001-1-11000000
χ61444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000000000220000000000000000000000000000000000
χ6244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-2442222222200000000000000000000-2-20000000000000000000000000000000000
χ634444-4-4-4-444-4-4-20000-2-2222-2200-2-2220000000000000000000022−2222−2200−2−222−2−22200000000000000000000000000
χ644444-4-4-4-444-4-4-20000-2-2222-2200-2-22200000000000000000000−2222−22220022−2−222−2−200000000000000000000000000
χ654444-4-4-4-4-4-444-20000-2-2222-220022-2-20000000000000000000022−22−222200−2−22222−2−200000000000000000000000000
χ664444-4-4-4-4-4-444-20000-2-2222-220022-2-200000000000000000000−222222−220022−2−2−2−22200000000000000000000000000
χ6744-4-444-4-400004-4-4444-44-4-4-44000000-44-4400000000000000000000000000000000000000000000000000000000
χ6844-4-444-4-40000-244-4-4-22-2222-2000000-22-22004-400000000-2-2220000000000000000000000000000000000000000
χ6944-4-444-4-40000-244-4-4-22-2222-2000000-22-2200-440000000022-2-20000000000000000000000000000000000000000
χ7044-4-444-4-40000-2-4-444-22-2222-20000002-22-200000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ7144-4-444-4-40000-2-4-444-22-2222-20000002-22-2000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ7244-4-4-4-4440000400004-4-444-4-400000000000000000000000000000000000000000000000022−22−222200000000000000
χ7344-4-4-4-4440000400004-4-444-4-4000000000000000000000000000000000000000000000000−222222−2200000000000000
χ744-44-44-44-400004-44-44-44-44-4-44000000-444-400000000000000000000000000000000000000000000000000000000
χ754-44-44-44-40000-24-44-42-22-222-2000000-222-24-4000000-2-22200000000000000000000000000000000000000000000
χ764-44-44-44-40000-24-44-42-22-222-2000000-222-2-4400000022-2-200000000000000000000000000000000000000000000
χ774-44-44-44-40000-2-44-442-22-222-20000002-2-22000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ784-44-44-44-40000-2-44-442-22-222-20000002-2-220000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ794-44-4-44-44000040000-444-44-4-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ804-44-4-44-44000040000-444-44-4-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ814-4-444-4-444-44-4-24-4-442222-2-2-24-4-22-22-2-22200000000000000000000-220000000000000000000000000000000000
χ824-4-444-4-44-44-44-24-4-442222-2-2-2-442-22-2-2-222000000000000000000002-20000000000000000000000000000000000
χ834-4-44-444-44-4-4440000-4-444-44-4004-4-44000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-44-4-44-2000022-2-22-2200-222-200000000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ854-4-44-444-44-4-44-2000022-2-22-2200-222-200000000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ864-4-44-444-4-444-440000-4-444-44-400-444-4000000000000000000000000000000000000000000000000000000000000
χ874-4-44-444-4-444-4-2000022-2-22-22002-2-2200000000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ884-4-44-444-4-444-4-2000022-2-22-22002-2-2200000000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ8988-8-8-8-8880000-40000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-880000-400004-4-44-444000000000000000000000000000000000000000000000000000000000000000000

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