Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61327 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1802 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)(13,16)(17,18)(22,28)(23,30)(25,32)(27,34)(29,31)(33,35);(12,13,15,16)(14,18,19,17)(20,21)(22,25)(23,27)(24,26)(28,32)(29,33)(30,34)(31,35);(20,22,24,29)(21,25,26,33)(23,31,30,28)(27,35,34,32);(12,14,15,19)(13,17,16,18);(21,26)(25,33)(27,34)(32,35)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54315);