Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1852 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)(20,21)(22,25)(23,31)(24,28)(26,30)(27,32)(29,34)(33,35);(12,13,15,16)(14,18,19,17)(20,22,25,21)(23,29,33,27)(24,28,26,30)(31,32,35,34);(20,23)(21,27)(22,29)(24,32)(25,33)(26,34)(28,35)(30,31);(12,14,15,19)(13,17,16,18)(21,22)(27,29)(28,30)(31,35);(20,24,25,26)(21,28,22,30)(23,32,33,34)(27,35,29,31)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54325);