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×#61670 |
| 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 | |
2102 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)(20,21,24,29)(22,31,32,26)(23,28,34,35)(25,27,33,30);(12,14)(13,16)(15,19)(17,18)(20,22)(21,26)(23,25)(24,32)(27,35)(28,30)(29,31)(33,34);(21,27)(22,32)(25,33)(26,28)(29,30)(31,35);(14,19)(16,18)(20,23)(21,28)(22,33)(24,34)(25,32)(26,27)(29,35)(30,31);(13,17)(16,18)(21,29)(22,32)(23,34)(27,30)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54658);