Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
848 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)(13,17)(15,22)(18,24)(19,23)(21,26)(25,27)(28,29,34,31)(30,38,41,43)(32,37,33,36)(35,42,39,40);(12,13,16,19)(14,18,20,25)(15,23,22,17)(21,27,26,24)(28,30,34,41)(29,35,31,39)(32,40,33,42)(36,38,37,43);(12,14,16,20)(13,18,19,25)(15,21,22,26)(17,24,23,27)(28,31,34,29)(30,39,41,35)(32,36,33,37)(38,42,43,40);(14,20)(18,25)(21,26)(24,27)(28,32,34,33)(29,36,31,37)(30,40,41,42)(35,38,39,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11430);