Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
508 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)(20,21,25,29)(22,30,32,35)(23,28,24,27)(26,33,34,31)(36,37,41,45)(38,46,49,50)(39,44,40,43)(42,48,51,47);(20,22,25,32)(21,26,29,34)(23,33,24,31)(27,35,28,30)(36,38,41,49)(37,42,45,51)(39,48,40,47)(43,50,44,46);(20,22)(21,26)(23,31)(24,33)(25,32)(27,30)(28,35)(29,34)(38,47)(39,40)(42,46)(43,44)(48,49)(50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3186);