Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
610 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)(16,17,21,24)(18,25,27,30)(19,23,20,28)(22,29,31,26)(32,33)(34,37)(35,38)(36,39)(40,43)(41,44)(42,46)(45,47);(16,18,21,27)(17,22,24,31)(19,26,20,29)(23,30,28,25)(32,34,36,41)(33,37,39,44)(35,40,42,47)(38,45,46,43);(13,15)(16,19,21,20)(17,23,24,28)(18,26,27,29)(22,30,31,25)(32,35)(33,38)(34,40)(36,42)(37,43)(39,46)(41,47)(44,45)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2917);