Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1322 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)(20,21)(22,30,33,26)(23,35,36,27)(24,29)(25,28)(31,38,42,34)(32,41)(37,48,49,43)(39,40)(44,47)(45,50)(46,51);(20,22,25,33)(21,26,28,30)(23,32,36,47)(24,38,40,34)(27,41,35,44)(29,31,39,42)(37,50,49,46)(43,45,48,51);(20,21)(22,31)(23,27)(24,39)(25,28)(26,38)(29,40)(30,34)(32,45)(33,42)(35,36)(37,48)(41,50)(43,49)(44,46)(47,51);(20,23)(21,27)(22,32)(24,37)(25,36)(26,41)(28,35)(29,43)(30,44)(31,45)(33,47)(34,46)(38,50)(39,48)(40,49)(42,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17398);