Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#538 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
1080 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)(20,21,23,28,25,29,34,42)(22,27,32,40,30,41,44,51)(24,26,33,37,35,38,47,49)(31,36,45,48,43,39,46,50);(21,26)(22,30)(23,33)(27,39)(29,38)(31,43)(32,46)(34,47)(36,41)(40,51)(44,45)(48,50);(20,22)(21,27)(23,32)(24,31)(25,30)(26,36)(28,40)(29,41)(33,45)(34,44)(35,43)(37,48)(38,39)(42,51)(46,47)(49,50);(22,31)(27,36)(30,43)(32,45)(39,41)(40,48)(44,46)(50,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10374);