Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(24,25)(26,34)(27,38,40,31)(28,41)(29,33)(30,36)(32,43)(35,49,51,48)(37,47)(39,46,55,53)(42,45)(44,50,52,54);(20,21)(22,23)(24,26,29,37)(25,30,33,45)(27,35,40,51)(28,42,43,36)(31,44,38,52)(32,47,41,34)(39,54,55,50)(46,49,53,48);(21,23)(24,27)(25,31)(26,35)(28,39)(29,40)(30,44)(32,46)(33,38)(34,48)(36,50)(37,51)(41,53)(42,54)(43,55)(45,52)(47,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3973);