Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13384 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25)(26,30)(27,31)(28,33)(29,35)(32,40)(34,41)(36,49)(37,46)(38,44)(39,45)(42,48)(43,50)(47,53)(51,55)(52,54);(20,21)(22,23)(24,26)(25,30)(27,37)(28,36)(29,39)(31,46)(32,43)(33,49)(34,44)(35,45)(38,41)(40,50)(42,51)(47,54)(48,55)(52,53);(20,22,23,21)(25,31)(26,36)(27,40)(28,41)(30,43)(32,34)(33,47)(35,48)(37,51)(38,39)(42,53)(44,55)(45,54)(46,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6372);