Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33401 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | C22×D4 |
| commutator | C4 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×C4⋊C8 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C2×C19×#131 ◁ G | |
684 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)(20,21,25,31,26,30,36,46,27,32,35,28,24,41,22,33)(23,29,39,45,40,44,48,51,37,43,49,42,38,50,34,47);(20,22,24,35,27,36,26,25)(21,28,30,33,32,31,41,46)(23,34,38,49,37,48,40,39)(29,42,44,47,43,45,50,51);(20,23)(21,29)(22,34)(24,38)(25,39)(26,40)(27,37)(28,42)(30,44)(31,45)(32,43)(33,47)(35,49)(36,48)(41,50)(46,51);(23,37)(29,43)(34,48)(38,40)(39,49)(42,45)(44,50)(47,51)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26389);