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×#18950 |
| 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 | |
824 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)(14,21)(15,18)(16,20)(17,25)(19,23)(22,26)(24,27)(29,34)(30,37)(31,32)(36,40)(38,39)(41,42);(12,14)(13,19)(15,22)(16,23)(17,26)(18,24)(20,27)(21,25)(28,29,33,36)(30,35,39,43)(31,34,32,40)(37,41,38,42);(12,15,18,13)(14,22,24,19)(16,20,17,25)(21,23,27,26)(28,30,33,39)(29,35,36,43)(31,37,32,38)(34,41,40,42);(12,16,18,17)(13,20,15,25)(14,23,24,26)(19,27,22,21)(28,31,33,32)(29,34,36,40)(30,38,39,37)(35,42,43,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11938);