Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21484 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#120 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C4×#120 |
| prime radical | C11×#3025 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C8×C11 ◁ G | |
1306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,16,18,21,30,29)(14,19,25,23,24,32,39,38)(15,20,28,26,27,33,41,40)(22,34,37,43,36,31,42,35);(12,14)(13,19)(15,22)(16,23)(17,25)(18,24)(20,31)(21,32)(26,35)(27,36)(28,37)(29,38)(30,39)(33,34)(40,43)(41,42);(12,15)(13,20)(14,22)(16,26)(17,28)(18,27)(19,31)(21,33)(23,35)(24,36)(25,37)(29,40)(30,41)(32,34)(38,43)(39,42);(12,16,17,21,18,29,30,13)(14,23,25,32,24,38,39,19)(15,26,28,33,27,40,41,20)(22,35,37,34,36,43,42,31)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14472);