Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11867 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1519 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C2×M16 | C23×C11 |
| prime radical | C11×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#131 ◁ G | |
372 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)(12,13,16,22,18,24,17,23)(14,25,28,20,29,38,26,39)(15,19,32,35,33,36,30,21)(27,40,42,34,31,37,43,41);(13,19)(14,26)(15,30)(16,17)(20,37)(21,23)(22,35)(24,36)(25,34)(28,29)(32,33)(38,41)(39,40)(42,43);(12,14,17,26,18,29,16,28)(13,20,22,38,24,39,23,25)(15,31,32,43,33,27,30,42)(19,34,21,40,36,41,35,37)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4860);