Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17767 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(36,37,40,45,41,43,39,44)(38,46,47,42,49,51,48,50);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(36,38)(37,42)(39,47)(40,48)(41,49)(43,50)(44,51)(45,46);(20,21)(22,26)(23,32)(24,27)(25,28)(29,30)(31,35)(33,34)(37,43)(42,50)(44,45)(46,51);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,39,41,40)(37,44,43,45)(38,47,49,48)(42,51,50,46)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10755);