Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19048 |
| 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 | |
908 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,24)(15,26)(16,21)(17,22)(18,23)(19,25)(20,27)(29,33)(31,38)(34,42)(35,39)(36,40)(41,43);(12,14,18,15)(13,19,23,20)(16,27,17,25)(21,24,22,26)(28,29,32,35)(30,34,37,43)(31,39,38,33)(36,41,40,42);(12,15,18,14)(13,20,23,19)(16,27,17,25)(21,24,22,26)(28,30,32,37)(29,34,35,43)(31,40,38,36)(33,41,39,42);(12,16,18,17)(13,21,23,22)(14,25,15,27)(19,26,20,24)(29,35)(33,39)(34,43)(41,42)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12036);