Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1804 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
412 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)(22,32,35,49)(23,29)(24,28)(25,41)(26,31)(27,33,44,36)(30,39)(34,47,38,43)(37,45)(40,46)(42,51,48,50);(20,22)(21,27,31,44)(23,33)(24,38)(25,36)(26,35)(28,42,46,48)(29,32,41,49)(30,47,45,43)(34,40)(37,51)(39,50);(21,28)(23,25)(24,39)(27,42)(29,30)(31,46)(32,47)(33,36)(34,51)(37,40)(38,50)(41,45)(43,49)(44,48)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5814);