Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1874 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
492 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)(20,21,25,30,26,32,41,44,27,33,23,39,24,31,40,28)(22,34,37,43,36,47,51,48,38,49,35,50,42,29,45,46);(21,28,33,44)(23,40)(24,26)(25,41)(29,43,47,50)(30,32,39,31)(34,46,49,48)(35,45)(36,42)(37,51);(20,22)(21,29)(23,37)(24,42)(25,35)(26,36)(27,38)(28,43)(30,48)(31,49)(32,34)(33,47)(39,46)(40,51)(41,45)(44,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5993);