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×#17625 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
1002 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)(22,28,30,25)(23,31)(24,27)(26,32)(29,33,35,34)(36,37)(38,45)(39,44)(40,48)(41,43)(42,46)(47,51)(49,50);(20,22)(21,25)(23,29)(24,30)(26,33)(27,28)(31,34)(32,35)(36,38)(37,42)(39,46)(40,49)(41,47)(43,50)(44,51)(45,48);(20,23)(21,26)(22,29)(24,32)(25,33)(27,31)(28,34)(30,35)(37,43)(42,50)(44,48)(45,51);(23,32)(26,31)(29,35)(33,34)(36,39,41,40)(37,44,43,48)(38,46,47,49)(42,51,50,45)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10613);