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×#18932 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
892 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)(13,17)(15,22)(18,24)(19,23)(21,26)(25,27)(28,29)(30,36)(31,39)(32,34)(33,38)(35,40)(37,43)(41,42);(12,13,16,19)(14,18,20,25)(15,23,22,17)(21,27,26,24)(31,40)(35,39)(36,43)(38,41);(12,14)(13,18)(15,21)(16,20)(17,24)(19,25)(22,26)(23,27)(28,30)(29,33)(31,41)(32,37)(34,42)(35,43)(36,39)(38,40);(14,20)(18,25)(21,26)(24,27)(29,34)(33,42)(35,39)(36,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11920);