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×#60036 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1820 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)(14,18)(15,17)(16,19)(28,29,33,32)(30,31,35,34);(12,13,15,17)(14,16,19,18)(22,26)(25,27)(30,35)(31,34);(20,21,24,23)(22,25,26,27)(28,30,33,35)(29,34,32,31);(12,13)(14,16)(15,17)(18,19)(20,22)(21,25)(23,27)(24,26)(28,31)(29,30)(32,35)(33,34);(12,14,15,19)(13,16,17,18)(20,23,24,21)(22,27,26,25)(28,32,33,29)(30,31,35,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53024);