Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
512 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)(12,13,15,18,16,14,17,19)(20,21)(22,25)(23,31,34,29)(24,30)(26,28)(27,33,35,32);(12,14,15,19,16,13,17,18)(20,22,25,21,26,30,24,28)(23,29,32,27,34,31,33,35);(20,23,26,34)(21,27,28,35)(22,29,30,31)(24,33,25,32)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2078);