Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17599 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3519 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
1046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29)(30,36,38,43)(31,35)(32,34)(33,37,41,39)(40,42);(12,14)(13,17)(15,21)(16,22)(18,24)(19,20)(23,27)(25,26)(28,30)(29,33)(31,39)(32,38)(34,41)(35,43)(36,42)(37,40);(15,23)(18,25)(21,27)(24,26)(29,34)(33,41)(35,42)(36,43);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10587);