Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36674 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,32)(31,33)(34,35)(36,37)(38,42)(39,43)(40,41)(44,47)(45,49)(46,48)(50,51);(30,34)(32,35)(37,41)(42,47)(43,48)(49,51);(20,22,23,27)(21,24,25,26)(28,30)(29,32)(31,34)(33,35)(36,38)(37,42)(39,45)(40,44)(41,47)(43,49)(46,50)(48,51);(29,33)(30,34)(38,44)(42,47)(45,50)(49,51);(36,39,40,46)(37,43,41,48)(38,45,44,50)(42,49,47,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29662);