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×#18965 |
| 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 | |
900 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)(14,23)(15,20)(16,21)(17,26)(18,22)(19,24)(25,27)(30,37)(31,32)(34,41)(35,39)(38,40)(42,43);(12,14,18,15)(13,19,22,27)(16,24,17,25)(20,26,23,21)(28,29)(30,34)(31,35)(32,39)(33,36)(37,42)(38,43)(40,41);(12,15,18,14)(13,20,22,23)(16,24,17,25)(19,26,27,21)(28,30)(29,34)(31,37)(32,40)(33,38)(35,42)(36,43)(39,41);(12,16,18,17)(13,21,22,26)(14,24,15,25)(19,20,27,23)(28,31,33,32)(29,35,36,39)(30,37,38,40)(34,42,43,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11953);