Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
2162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
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)(22,30)(23,24)(26,33)(28,29)(31,32)(34,35);(12,14,15,19)(13,16,17,18)(20,21)(22,26)(23,28)(24,29)(25,27)(30,33)(31,34)(32,35);(14,19)(16,18)(20,22)(21,26)(23,30)(24,32)(25,31)(27,34)(28,33)(29,35);(13,17)(16,18)(21,27)(26,34)(28,29)(33,35);(20,23,25,24)(21,28,27,29)(22,30,31,32)(26,33,34,35)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53796);