Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11597 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #102 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C2×C11×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21)(22,31,34,48)(23,27)(24,38)(25,30)(26,33,42,50)(28,36)(29,37)(32,47,35,44)(39,46,51,41)(40,43)(45,49);(20,22)(21,26)(23,32)(24,39)(25,34)(27,41)(28,44)(29,46)(30,42)(31,43)(33,49)(35,37)(36,50)(38,48)(40,51)(45,47);(20,23,25,37)(21,27,30,29)(22,32,34,35)(24,36,40,49)(26,41,42,46)(28,43,45,38)(31,47,48,44)(33,39,50,51)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4585);