Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10159 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,14)(15,18,16,19)(22,28)(23,30)(25,33)(26,31)(29,32)(34,35);(13,18)(14,19)(15,16)(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33);(12,14,17,13)(15,19,16,18)(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,30)(31,33)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3147);