Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33350 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×D4×C19 ◁ C2×C19×H(5,𝔽2) ◁ G | |
1240 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)(24,36,37,28)(25,29)(26,32,39,46)(31,42)(33,43)(34,40)(35,48,47,41)(38,45,49,51)(44,50);(20,22,25,33)(21,26,29,39)(23,31,34,44)(24,32,37,46)(27,38,40,49)(28,30,36,43)(35,45,47,51)(41,42,48,50);(20,23)(21,27)(22,31)(24,35)(25,34)(26,38)(28,41)(29,40)(30,42)(32,45)(33,44)(36,48)(37,47)(39,49)(43,50)(46,51);(23,34)(27,40)(31,44)(35,47)(38,49)(41,48)(42,50)(45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26338);