Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3487 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1258 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)(20,21,25,31,26,30,23,28)(22,32,33,41,35,27,39,43)(24,37,36,45,38,29,40,44)(34,42,49,50,48,46,47,51);(20,22)(21,27)(23,33)(24,34)(25,39)(26,35)(28,43)(29,42)(30,32)(31,41)(36,47)(37,46)(38,48)(40,49)(44,51)(45,50);(20,23,26,25)(21,28,30,31)(22,33,35,39)(24,36,38,40)(27,41,32,43)(29,44,37,45)(34,47,48,49)(42,50,46,51);(20,24,26,38)(21,29,30,37)(22,34,35,48)(23,36,25,40)(27,42,32,46)(28,44,31,45)(33,47,39,49)(41,50,43,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14769);