Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18944 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
880 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)(21,25)(23,30)(26,32)(27,31)(29,34)(33,35)(36,37)(38,46)(39,42)(40,45)(41,44)(43,49)(47,50)(48,51);(20,21,24,27)(22,26,28,33)(23,31,30,25)(29,35,34,32)(37,42)(39,40)(43,50)(44,45)(46,51)(48,49);(20,22)(21,26)(23,29)(24,28)(25,32)(27,33)(30,34)(31,35)(36,38)(37,43)(39,49)(40,48)(41,47)(42,50)(44,51)(45,46);(22,28)(26,33)(29,34)(32,35)(37,44)(38,47)(42,45)(48,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11932);