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×#33561 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1096 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)(23,28)(24,29)(25,30)(26,31)(27,34)(33,44)(35,42)(36,41)(37,45)(38,46)(39,47)(40,48)(43,49)(50,51);(20,22,26,23)(21,27,31,41)(24,35,38,33)(25,34,39,36)(28,30,32,47)(29,43,46,40)(37,49,50,48)(42,51,44,45);(20,23,26,22)(21,28,31,32)(24,33,38,35)(25,34,39,36)(27,30,41,47)(29,44,46,42)(37,49,50,48)(40,51,43,45);(20,24,26,38)(21,29,31,46)(22,33,23,35)(25,37,39,50)(27,40,41,43)(28,42,32,44)(30,45,47,51)(34,48,36,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26549);