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) = C24 |
| direct product | C11×#11369 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #399 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
602 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)(18,26,29,39)(19,23)(20,24)(21,25)(22,28,35,32)(27,42,44,41)(30,37)(31,38)(33,40)(34,45,36,43)(46,47);(13,15)(16,18,20,32,21,29,33,28)(17,22,24,39,25,35,40,26)(19,27,30,45,31,44,46,43)(23,36,37,41,38,34,47,42);(13,15)(16,19,20,30,21,31,33,46)(17,23,24,37,25,38,40,47)(18,27,32,45,29,44,28,43)(22,34,39,42,35,36,26,41)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4357);