Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#20776 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#383 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×M16×C19 ◁ 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)(22,31)(23,35,37,42)(24,29)(25,30)(26,34)(27,36,43,49)(28,38)(32,39,45,50)(33,41)(40,47)(44,46,48,51);(20,22,25,33)(21,26)(23,32,37,45)(24,34,38,47)(27,39)(28,31)(29,41)(30,40)(35,48)(36,46,49,51)(42,44)(43,50);(20,23,24,36,25,37,38,49)(21,27,28,42,30,43,29,35)(22,32,34,46,33,45,47,51)(26,39,31,44,40,50,41,48);(22,33)(26,40)(31,41)(32,45)(34,47)(39,50)(44,48)(46,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13764);