Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,27)(24,29)(25,30)(28,32)(31,42)(33,40)(34,51)(35,43)(36,44)(37,46)(38,47)(39,48)(41,50)(45,49);(20,22)(21,26)(23,34,35,50)(24,33)(25,32)(27,41,43,51)(28,30)(29,40)(31,36,48,37)(38,49)(39,44,42,46)(45,47);(20,23)(21,27)(22,31)(24,37)(25,35)(26,39)(28,42)(29,46)(30,43)(32,48)(33,50)(34,49)(36,38)(40,51)(41,45)(44,47);(20,22)(21,28)(23,31)(24,33)(25,32)(26,30)(27,42)(29,45)(34,36)(35,48)(37,50)(38,49)(39,43)(40,47)(41,46)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16983);