Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29,33,37)(30,38,41,42)(31,36,32,35)(34,39,43,40);(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(28,30)(29,34)(31,39)(32,40)(33,41)(35,42)(36,38)(37,43);(12,13)(14,18)(15,24)(16,19)(17,20)(21,22)(23,27)(25,26)(29,35)(31,32)(34,42)(36,37)(38,43)(39,40);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,31,33,32)(29,35,37,36)(30,39,41,40)(34,42,43,38)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11937);