Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1864 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
384 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)(21,26,29,28)(22,31,32,50)(23,34)(24,38)(27,42)(30,47,39,35)(33,36,40,51)(37,49)(41,43)(44,46);(20,21,24,39,25,29,38,30)(22,27,40,45,32,42,33,48)(23,35,34,26,37,47,49,28)(31,46,36,44,50,41,51,43);(20,22)(21,27)(23,36)(24,40)(25,32)(26,41)(28,46)(29,42)(30,48)(31,49)(33,38)(34,50)(35,44)(37,51)(39,45)(43,47)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5940);