Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#32951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1298 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)(22,31)(24,27)(29,39)(30,40)(32,47)(33,34)(35,36)(38,42)(41,50)(44,45)(46,48);(20,21,27,40,25,30,24,26)(22,28,31,42,34,43,33,38)(23,29,36,44,37,45,35,39)(32,41,46,51,48,50,47,49);(20,22)(21,28)(23,32)(24,33)(25,34)(26,38)(27,31)(29,41)(30,43)(35,47)(36,46)(37,48)(39,49)(40,42)(44,51)(45,50);(20,23)(21,29)(22,32)(24,35)(25,37)(26,39)(27,36)(28,41)(30,45)(31,46)(33,47)(34,48)(38,49)(40,44)(42,51)(43,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25939);