Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13110 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×D8 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,21)(19,20)(22,23)(24,25)(26,29)(27,30)(28,36)(31,35)(32,34)(33,37)(38,39);(12,14,15,13)(17,20)(21,23)(25,29)(30,37)(31,38)(32,36);(16,18,19,22)(17,21,20,23)(25,30)(27,35)(28,34)(29,37)(31,32)(33,39)(36,38)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6098);