Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11111 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #392 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
874 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)(12,13,14,15)(16,17)(18,28)(19,32)(20,26)(21,25)(22,27)(23,30)(24,33)(29,37)(31,41)(34,42)(35,38)(36,40)(39,46)(43,45)(44,47);(16,18,20,30,22,31,21,35)(17,23,25,28,27,38,26,41)(19,29,33,44,34,46,36,45)(24,39,32,47,40,37,42,43);(16,19)(17,24)(18,29)(20,33)(21,36)(22,34)(23,37)(25,32)(26,42)(27,40)(28,43)(30,44)(31,46)(35,45)(38,39)(41,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4099);