Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10974 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1258 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)(20,21)(22,23)(24,25,28,33,29,32,41,47)(26,34,36,48,37,30,40,43)(27,31,39,46,38,45,51,55)(35,44,50,54,49,42,52,53);(24,26,29,37)(25,30,32,34)(27,35,38,49)(28,40,41,36)(31,44,45,42)(33,48,47,43)(39,52,51,50)(46,53,55,54);(21,23)(24,27)(25,31)(26,35)(28,39)(29,38)(30,42)(32,45)(33,46)(34,44)(36,50)(37,49)(40,52)(41,51)(43,53)(47,55)(48,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3962);