Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#12616 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C42 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×#97 |
| prime radical | C24×C11 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
420 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)(16,17,20,26,21,23,29,30,22,18,24,27,19,25,28,31);(13,15)(17,23,18,25)(20,24)(26,31,27,30)(28,29);(16,18,20,27,21,25,29,31,22,17,24,26,19,23,28,30)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5604);