Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#8254 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C23×C11 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
394 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)(16,18)(17,19)(20,21,25,29,26,30,24,34)(22,23,28,27,31,33,35,32);(12,14,16,19,17,18,15,13)(20,22,25,28,26,31,24,35)(21,27,29,33,30,32,34,23);(12,15,17,16)(13,14,19,18)(20,23,24,32,26,33,25,27)(21,28,34,22,30,35,29,31)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1242);