Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61643 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61673 |
| 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 | |
2160 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)(28,31)(30,35)(32,34);(12,14)(13,16)(15,19)(17,18)(20,21)(22,30)(23,26)(24,33)(25,27)(28,32)(29,31)(34,35);(20,22)(21,28)(23,31)(24,29)(25,32)(26,34)(27,30)(33,35);(14,19)(16,18)(20,23)(21,24)(22,31)(25,33)(26,27)(28,29)(30,34)(32,35);(13,17)(16,18)(20,24,25,26)(21,23,27,33)(22,29,32,34)(28,31,30,35)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54661);