Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,18)(16,19)(20,23)(21,24)(22,26)(25,27)(28,29,33,37)(30,38,41,42)(31,34,32,36)(35,39,43,40);(12,14,16,21)(13,17,19,24)(15,20,22,27)(18,25,26,23)(29,34)(31,32)(35,42)(36,37)(38,43)(39,40);(12,15)(13,18)(14,20)(16,22)(17,23)(19,26)(21,27)(24,25)(28,30,33,41)(29,35,37,43)(31,40,32,39)(34,42,36,38)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2949);