Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #58990 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#60041 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(21,25)(22,27)(28,29,33,31)(30,32,35,34);(14,18)(17,19)(21,25)(22,27)(28,30,33,35)(29,34,31,32);(12,13,16,15)(14,17,18,19)(20,21)(22,26)(23,27)(24,25)(28,31,33,29)(30,32,35,34);(12,14)(13,17)(15,19)(16,18)(20,22,24,27)(21,26,25,23);(12,15,16,13)(14,19,18,17)(20,23,24,26)(21,27,25,22)(28,32)(29,30)(31,35)(33,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53029);