Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#12053 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C2×D4 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle, prime radical | C22×C11 | C8×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C4×C11×C16 ◁ G | |
206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)(28,29,31,35,32,30,37,38,33,36,40,43,41,39,34,42);(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(28,30,31,38,32,36,37,43,33,39,40,42,41,29,34,35)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5041);