Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18521 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C19×#3480 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
936 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)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(36,37,42,47)(38,48,50,44)(39,51,49,43)(40,45,41,46);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,38)(37,43)(39,40)(41,49)(42,50)(44,46)(45,48)(47,51);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,39,42,49)(37,44,47,48)(38,40,50,41)(43,46,51,45);(36,40,42,41)(37,45,47,46)(38,39,50,49)(43,48,51,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11509);