Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#9080 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,19,22,20,18,21,23)(24,25,29,30,28,31,27,26);(16,18,19,23,20,17,21,22)(24,26,29,31,28,30,27,25);(13,15)(24,27,28,29)(25,30,31,26)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2068);