Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1674 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)(22,27)(23,34)(24,26)(25,30)(28,35)(29,37)(31,46)(32,41)(33,43)(36,45)(38,40)(39,44)(42,47)(48,50)(49,51);(21,26)(24,37)(27,41)(28,34)(29,30)(32,38)(35,39)(40,43)(42,46)(44,45)(47,49)(50,51);(20,22,25,33)(21,27,30,43)(23,31,36,48)(24,38,37,32)(26,40,29,41)(28,42,44,51)(34,50,45,46)(35,49,39,47);(20,23)(21,28)(22,31)(24,39)(25,36)(26,34)(27,42)(29,45)(30,44)(32,49)(33,48)(35,37)(38,47)(40,50)(41,46)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16862);