Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33569 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C19 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C23×C19 ◁ C22×Q8×C19 ◁ G | |
1082 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)(22,32)(23,29)(24,37)(25,40)(26,31)(27,33)(28,36)(30,42)(34,47)(35,50)(38,44)(39,46)(41,43)(45,51)(48,49);(20,22)(21,27)(23,33)(24,38)(25,41)(26,34)(28,43)(29,47)(30,45)(31,44)(32,37)(35,42)(36,51)(39,49)(40,48)(46,50);(20,23,26,24)(21,28,31,46)(22,33,34,38)(25,39,42,36)(27,43,44,50)(29,30,37,40)(32,48,47,45)(35,51,41,49);(22,34)(27,44)(32,47)(33,38)(35,41)(43,50)(45,48)(49,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26557);