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×#33558 |
| 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 ◁ C23×C19 ◁ C22×D4×C19 ◁ G | |
1158 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)(26,33)(31,43)(32,44)(34,40)(35,41)(36,49)(37,42)(38,45)(39,47)(46,51)(48,50);(20,22,25,32)(21,26,29,39)(23,31,34,46)(24,33,37,47)(27,38,40,50)(28,30,42,44)(35,45,36,48)(41,43,49,51);(20,23)(21,27)(22,31)(24,36)(25,34)(26,38)(28,41)(29,40)(30,43)(32,46)(33,48)(35,37)(39,50)(42,49)(44,51)(45,47);(22,32)(23,34)(26,39)(27,40)(30,44)(33,47)(35,36)(41,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26546);