Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#34184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
3006 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)(13,15)(16,17,18,19)(20,21)(22,28)(23,31)(24,25)(26,30)(27,32)(29,33)(34,35);(21,25)(26,28)(27,31)(33,34);(12,13,14,15)(20,22)(21,26)(23,29)(24,30)(25,28)(27,33)(31,34)(32,35);(20,21)(22,26)(23,27)(24,25)(28,30)(29,33)(31,32)(34,35);(20,23,24,32)(21,27,25,31)(22,29,30,35)(26,33,28,34)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27172);