Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33337 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×C22⋊C8 |
| prime radical | C22×#41×C19 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C19×#131 ◁ G | |
1128 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)(20,21,23,28,24,29,34,41,25,26,33,37,35,38,45,48)(22,27,31,39,32,40,44,49,30,36,42,46,43,47,50,51);(21,26)(23,33)(27,36)(29,38)(31,42)(34,45)(40,47)(44,50);(20,22)(21,27)(23,31)(24,32)(25,30)(26,36)(28,39)(29,40)(33,42)(34,44)(35,43)(37,46)(38,47)(41,49)(45,50)(48,51);(22,30)(27,36)(31,42)(32,43)(39,46)(40,47)(44,50)(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, 26325);