Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8674 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#8693 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #380 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,27,25,23,22,26)(28,29)(30,39)(31,44,46,51)(32,47)(33,37)(34,38)(35,41)(36,45,52,48)(40,49,56,59)(42,50)(43,54)(53,55,58,57);(20,22,25,24)(21,26,23,27)(28,30,33,42,34,43,32,41)(29,35,47,54,38,50,37,39)(31,40,48,57,46,56,45,55)(36,49,44,58,52,59,51,53);(20,23)(21,25)(22,27)(24,26)(28,31)(29,36)(30,40)(32,45)(33,48)(34,46)(35,49)(37,51)(38,52)(39,53)(41,55)(42,57)(43,56)(44,47)(50,59)(54,58)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1681);