Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
924 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,24,27)(22,25,29,32)(23,26,30,33)(28,34,35,31)(37,42)(39,40)(43,50)(44,48)(45,46)(49,51);(20,22)(21,25)(23,28)(24,29)(26,31)(27,32)(30,35)(33,34)(36,37)(38,43)(39,42)(40,48)(41,44)(45,50)(46,49)(47,51);(20,23)(21,26)(22,28)(24,30)(25,31)(27,33)(29,35)(32,34)(36,38,41,47)(37,43,44,51)(39,46,40,45)(42,49,48,50);(36,39,41,40)(37,42,44,48)(38,45,47,46)(43,50,51,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11257);