Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#32701 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C24×C11 ◁ G | |
628 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)(14,22,25,18)(15,26,29,19)(16,20)(17,21)(23,36)(24,32,38,34)(27,31)(28,39,41,33)(30,35)(37,42)(40,43);(12,14)(13,18)(15,27)(16,24)(17,25)(19,31)(20,34)(21,22)(23,29)(26,36)(28,40)(30,38)(32,35)(33,43)(37,41)(39,42);(12,15)(13,19)(14,23,25,27)(16,28)(17,29)(18,31,22,36)(20,33)(21,26)(24,37,38,40)(30,41)(32,42,34,43)(35,39);(12,16,17,30)(13,20,21,35)(14,24,25,38)(15,28,29,41)(18,32,22,34)(19,33,26,39)(23,37,27,40)(31,42,36,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25689);