Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18240 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1056 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(21,26)(23,33)(27,38)(28,37)(29,34)(31,42)(35,47)(39,44)(40,49)(41,48)(45,46)(50,51);(20,21)(22,27)(23,34)(24,29)(25,28)(26,33)(30,39)(31,44)(32,40)(35,48)(36,41)(37,47)(38,42)(43,51)(45,49)(46,50);(22,30)(23,35)(26,37)(27,39)(31,45)(32,43)(33,47)(34,48)(38,50)(40,51)(42,46)(44,49);(20,22,25,32)(21,27,28,40)(23,31,35,46)(24,30,36,43)(26,38,37,49)(29,39,41,51)(33,42,47,45)(34,44,48,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11228);