Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
746 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)(20,21,24,26)(22,27,23,25)(28,29,31,33)(30,34,35,32)(36,37,41,45)(38,42,48,51)(39,43,40,44)(46,49,47,50);(20,22,24,23)(21,25,26,27)(28,30,31,35)(29,32,33,34)(36,38)(37,42)(39,47)(40,46)(41,48)(43,50)(44,49)(45,51);(29,33)(32,34)(38,46)(39,40)(42,49)(43,44)(47,48)(50,51);(20,23,24,22)(21,25,26,27)(36,39,41,40)(37,43,45,44)(38,47,48,46)(42,50,51,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16814);