Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#22462 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | D4×C22⋊C4 |
| prime radical | C11×#3584 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
1320 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)(12,13,18,22)(14,23,27,25)(15,28)(16,31,17,21)(19,32,35,26)(20,33)(24,39)(29,37)(30,36)(34,43)(38,41)(40,42);(12,14)(13,19)(15,24)(16,32)(17,26)(18,27)(20,34)(21,25)(22,35)(23,31)(28,38)(29,42)(30,43)(33,41)(36,40)(37,39);(12,15)(13,20)(14,24)(16,29)(17,33)(18,30)(19,34)(21,36)(22,37)(23,38)(25,40)(26,41)(27,43)(28,31)(32,42)(35,39);(12,13)(14,25)(15,20)(16,31)(17,21)(18,22)(19,32)(23,27)(24,40)(26,35)(28,29)(30,37)(33,36)(34,42)(38,43)(39,41)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15450);