Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22251 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C43×C11 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,20)(18,22)(21,23)(24,25)(26,33)(27,31)(28,37)(29,32)(30,35)(34,39)(36,38);(12,14,15,13)(16,17,19,20)(18,22,23,21)(24,26)(25,30)(27,36)(28,34)(29,35)(31,39)(32,33)(37,38);(16,18,17,21,19,23,20,22)(24,27,29,28)(25,31,32,37)(26,34,35,36)(30,38,33,39);(16,17,19,20)(18,22,23,21)(24,28,29,27)(25,31,32,37)(26,34,35,36)(30,39,33,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15239);