Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9183 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#9195 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C24×C19 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
524 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)(20,21,22,25,23,26,27,24)(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);(21,24)(22,27)(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);(28,31)(29,35)(30,39)(32,46)(33,44)(34,48)(36,51)(37,42)(38,52)(40,56)(41,55)(43,47)(45,50)(49,58)(53,59)(54,57)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2183);