Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G | |
1824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(20,21)(22,27)(23,32)(24,28)(25,33)(26,29)(30,34)(31,35);(13,15)(16,17)(18,19)(20,22,26,31)(21,27,29,35)(23,25,30,24)(28,32,33,34);(17,19)(20,23)(21,27)(22,24)(25,31)(26,30)(28,34)(29,35)(32,33);(13,15)(20,24,26,25)(21,28,29,33)(22,30,31,23)(27,34,35,32)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16917);