Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22478 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G | |
1132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21)(22,26)(23,31,33,27)(24,28)(25,29)(30,35,32,34);(12,13)(14,17)(15,16)(18,19)(20,22,25,24)(21,26,29,28)(23,30,33,32)(27,34,31,35);(12,14,15,18)(13,17,16,19)(20,23)(21,27)(22,30)(24,32)(25,33)(26,34)(28,35)(29,31);(13,16)(17,19)(20,24,25,22)(21,28,29,26)(23,32,33,30)(27,35,31,34)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15466);