Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
536 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)(22,26)(23,25)(24,28)(27,31)(29,34)(30,35)(32,33)(36,37,41,45)(38,46,48,51)(39,44,40,43)(42,49,50,47);(21,25)(23,31)(26,34)(27,28)(29,32)(33,35)(36,38)(37,42)(39,49)(40,47)(41,48)(43,51)(44,46)(45,50);(20,22,24,30)(21,26,28,35)(23,32,31,29)(25,33,27,34)(37,43)(39,40)(42,46)(44,45)(47,49)(50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3237);