Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11241 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #380 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,26)(19,23,31,37)(20,32)(21,25)(22,28)(24,33)(27,38,41,47)(29,39)(30,43,44,36)(34,45,46,40)(35,42);(12,13)(14,15)(16,18,20,28,21,29,33,42)(17,22,24,26,25,35,32,39)(19,27,30,40,31,41,44,45)(23,34,36,38,37,46,43,47);(13,15)(16,19,20,30,21,31,33,44)(17,23,24,36,25,37,32,43)(18,27,28,40,29,41,42,45)(22,34,26,38,35,46,39,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4229);