Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,27)(23,29)(24,28)(25,30)(26,31)(32,35)(33,34)(36,37,41,45)(38,46,49,50)(39,44,40,43)(42,47,51,48);(20,22)(21,26)(23,31)(24,33)(25,32)(27,28)(29,35)(30,34)(36,38)(37,42)(39,47)(40,48)(41,49)(43,50)(44,46)(45,51);(20,22)(21,27)(23,33)(24,31)(25,32)(26,28)(29,34)(30,35)(37,43)(39,40)(42,50)(44,45)(46,51)(47,48);(20,23,25,24)(21,28,30,29)(22,31,32,33)(26,27,34,35)(36,39,41,40)(37,43,45,44)(38,47,49,48)(42,50,51,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11710);