Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #20338 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33329 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×C42 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×#97 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ G | |
716 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)(20,21,23,28,24,30,35,43,25,29,34,44,36,26,37,39)(22,27,32,41,33,42,47,51,31,40,45,50,46,38,48,49);(21,26,29,30)(23,34)(27,38,40,42)(28,43,44,39)(32,45)(35,37)(41,51,50,49)(47,48);(20,22)(21,27)(23,32)(24,33)(25,31)(26,38)(28,41)(29,40)(30,42)(34,45)(35,47)(36,46)(37,48)(39,49)(43,51)(44,50);(22,31)(27,40)(32,45)(33,46)(38,42)(41,50)(47,48)(49,51)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26317);