Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9159 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9178 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,25,29,35)(23,28)(24,27)(26,30,34,31)(32,33)(36,37,40,44,41,45,39,43)(38,46,47,42,49,50,48,51);(20,22)(21,25,27,35)(23,31)(24,29)(26,33,34,28)(30,32)(36,38)(37,42)(39,47)(40,48)(41,49)(43,50)(44,46)(45,51);(20,22)(21,26)(23,31)(24,29)(25,33)(27,34)(28,35)(30,32)(36,39,41,40)(37,43,45,44)(38,47,49,48)(42,50,51,46)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2166);