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×#60012 |
| 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 | |
1662 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)(12,13)(14,15)(16,18)(17,19)(21,25)(23,27)(28,29)(30,33)(31,35)(32,34);(12,14,16,19)(13,15,18,17)(20,21,24,25)(22,23,26,27)(29,30)(34,35);(12,13,16,18)(14,17,19,15)(20,22,24,26)(21,23,25,27)(28,30,33,29)(31,35,32,34);(12,14)(13,17)(15,18)(16,19)(28,31,33,32)(29,34,30,35);(12,15,16,17)(13,14,18,19)(20,23)(21,26)(22,25)(24,27)(28,32,33,31)(29,35,30,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53000);