Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24985 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2420 |
| prime radical | C11×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
646 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)(14,26)(15,30)(16,20)(17,24)(18,23)(19,25)(21,33)(22,29)(27,42)(28,37)(31,39)(32,38)(34,40)(35,41)(36,43);(12,14,18,28,19,29,17,16)(13,20,24,22,25,37,23,26)(15,31,33,27,35,32,34,43)(21,38,30,42,40,39,41,36);(12,15)(13,21)(14,27)(16,32)(17,33)(18,34)(19,35)(20,36)(22,39)(23,30)(24,41)(25,40)(26,38)(28,31)(29,43)(37,42);(12,16,17,29,19,28,18,14)(13,22,23,20,25,26,24,37)(15,32,33,43,35,31,34,27)(21,39,30,36,40,38,41,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17973);