Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C19 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1132 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)(23,27)(24,28)(25,29)(26,32)(31,44)(33,45)(34,48)(35,41)(36,42)(37,43)(38,46)(39,47)(40,49)(50,51);(20,22,25,33)(21,26,29,39)(23,34,35,31)(24,32,37,47)(27,40,41,38)(28,30,43,45)(36,49,50,46)(42,48,51,44);(23,35)(24,37)(27,41)(31,34)(32,47)(38,40)(42,51)(44,48);(20,23,25,35)(21,27,29,41)(22,31,33,34)(24,36,37,50)(26,38,39,40)(28,42,43,51)(30,44,45,48)(32,46,47,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26548);