Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,18)(17,19)(20,21)(22,28,30,34)(23,26)(24,27)(25,31,29,32)(33,35);(20,21)(22,29,30,25)(23,26)(24,27)(28,31,34,32)(33,35);(13,16)(14,19)(17,18)(20,22)(21,25)(23,32)(24,30)(26,34)(27,29)(28,35)(31,33)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3362);