Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#12561 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C8 | C2×C42×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C24×C11 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
570 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)(18,27)(19,32)(20,35)(21,37)(22,26)(23,29)(24,34)(25,33)(28,41)(30,38)(31,47)(36,40)(39,46)(42,45)(43,44);(16,18,20,30,33,44,34,45,22,28,19,29,21,31,36,46)(17,23,24,27,37,42,35,47,26,38,40,41,25,39,32,43);(18,28)(23,38)(27,41)(29,30)(31,44)(39,42)(43,47)(45,46)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5549);