Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#12667 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #117 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1770 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C2×C19×M32 ◁ G | |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,30,26,31,40,46,24,29,37,45,39,23,28,38)(22,27,33,42,34,43,48,51,35,32,41,47,49,36,44,50);(20,22)(21,27,29,32)(23,36,31,43)(24,35)(25,33)(26,34)(28,44)(30,42,45,47)(37,41)(38,50,46,51)(39,49)(40,48);(20,23,37,46,26,21,28,45,24,31,25,38,39,29,40,30)(22,32,33,47,34,36,48,50,35,27,41,42,49,43,44,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5655);