Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#12569 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #102 |
| 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)(19,24)(20,34)(21,37)(22,26)(23,29)(25,35)(28,42)(30,40)(31,46)(32,39)(33,41)(36,47)(38,44)(43,45);(16,18,20,30,19,28,33,45,22,32,36,29,21,31,35,44)(17,23,25,39,37,43,47,42,26,40,41,27,24,38,34,46);(16,19,22,21)(17,24,26,37)(18,28,32,31)(20,33,36,35)(23,38,40,43)(25,34,41,47)(27,42,39,46)(29,44,30,45)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5557);