Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13201 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #390 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1955 |
| prime radical | C11×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C8×C11 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,23,18,22,37,41,19,24,38,27,16,21,26,32)(14,25,29,43,28,35,40,42,30,33,20,39,36,15,31,34);(12,14,26,40,16,36,38,29,19,30,37,31,18,28,17,20)(13,15,32,43,21,33,27,34,24,35,41,39,22,25,23,42);(12,15,16,33,19,35,18,25)(13,20,22,31,24,29,21,40)(14,27,28,32,30,23,36,41)(17,34,26,39,38,42,37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6189);