Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C4 |
| direct product | C11×#8297 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C2×D4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C4⋊C4 |
| prime radical | C23×C11 | C4×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14,16,17,19,18)(21,26,28,32)(22,29)(27,34,35,33)(30,31);(20,21,24,26,25,28,23,32)(22,27,31,33,29,35,30,34);(12,14,15,17,16,18,19,13)(20,22,23,30,25,29,24,31)(21,27,32,34,28,35,26,33)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1285);