Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9104 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,26,23,22,25,27)(28,29)(30,38)(31,42,44,35)(32,45)(33,37)(34,40)(36,47)(39,52,55,59)(41,53)(43,50,46,51)(48,54,58,56)(49,57);(20,22,24,27,23,21,25,26)(28,30,32,40,33,41,47,57)(29,34,36,38,37,49,45,53)(31,39,46,56,44,55,43,54)(35,48,51,52,42,58,50,59);(21,22)(26,27)(28,31,33,44)(29,35,37,42)(30,39,41,55)(32,46,47,43)(34,48,49,58)(36,51,45,50)(38,52,53,59)(40,56,57,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2092);