Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#8480 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C11×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
828 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15,18,19)(16,17)(20,21)(22,29,31,26)(23,25)(24,28)(27,32)(30,34,35,33);(12,14)(13,15)(16,18)(17,19)(21,25)(23,32)(26,33)(27,28)(29,34)(30,35);(12,15)(13,14)(16,19)(17,18)(20,22,24,31)(21,26,28,29)(23,30,32,35)(25,33,27,34)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1468);