Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1152 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)(20,21,24,26)(22,27,32,39)(23,33,34,28)(25,37,36,29)(30,40,38,42)(31,41,45,46)(35,43,48,47)(44,50,49,51);(21,26)(22,30,32,38)(27,40,39,42)(28,33)(29,37)(31,44,45,49)(41,50,46,51)(43,47);(20,22)(21,27)(23,31)(24,32)(25,38)(26,39)(28,41)(29,40)(30,36)(33,46)(34,45)(35,49)(37,42)(43,50)(44,48)(47,51);(20,23)(21,28)(22,31)(24,34)(25,35)(26,33)(27,41)(29,43)(30,44)(32,45)(36,48)(37,47)(38,49)(39,46)(40,50)(42,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16981);