Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#17971 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C19×#431 ◁ G | |
600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,31)(24,26)(25,29)(27,33)(30,35)(32,34)(36,37,41,44,40,43,49,51)(38,45,47,48,46,42,50,39);(20,22,24,30)(21,25,26,34)(23,32,33,29)(27,35,31,28)(36,38)(37,42)(39,44)(40,46)(41,47)(43,45)(48,51)(49,50);(20,21)(22,25)(23,27)(24,26)(28,29)(30,34)(31,33)(32,35)(36,39,41,45,40,48,49,42)(37,38,44,47,43,46,51,50);(21,26)(25,34)(27,31)(28,35)(37,43)(38,46)(44,51)(47,50)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10959);