Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61664 |
| 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×#532 ◁ G | |
2136 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)(12,13)(14,18)(15,17)(16,19)(21,27)(22,29)(24,26)(28,30)(31,33)(34,35);(12,14)(13,16)(15,19)(17,18)(20,21)(22,28)(23,26)(24,32)(25,27)(29,35)(30,33)(31,34);(20,22,25,31)(21,28,27,34)(23,30,32,35)(24,29,26,33);(14,19)(16,18)(20,23)(21,24)(22,30)(25,32)(26,27)(28,29)(31,35)(33,34);(13,17)(16,18)(20,24,25,26)(21,23,27,32)(22,29,31,33)(28,30,34,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54652);