Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#7451 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #357 |
| commutator | C2×C16 | C2×C4×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29,31,37,47,56,59,35,34,40,30,41,33,39,48,53,32,38,45,52,43,54,42,51,50,57,44,36,49,55,46,58);(20,21,23,25)(22,27,26,24)(29,35)(30,42)(31,46)(33,43)(34,50)(36,39)(37,56)(38,51)(40,58)(41,55)(44,59)(45,48)(47,49)(52,54)(53,57)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 439);