Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#36594 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,18)(19,21,23,22)(25,29)(26,31);(16,17,20,18)(19,22,23,21)(24,25)(26,30)(27,31)(28,29);(12,13,14,15)(17,18)(21,22)(24,26,28,31)(25,30,29,27);(16,18,20,17)(19,21,23,22)(24,27,28,30)(25,31,29,26);(16,19,20,23)(17,21,18,22)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29582);