Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#12005 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C2×D4 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×C4⋊C8 |
| prime radical | C23×C19 | C4⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ C2×C4×C8×C19 ◁ G | |
242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,25)(26,27)(28,29,31,35,32,36,41,47,33,37,42,48,43,49,53,57)(30,34,39,45,40,46,52,56,38,44,50,54,51,55,58,59);(20,21,25,27,23,26,22,24)(28,30)(29,34)(31,39)(32,40)(33,38)(35,45)(36,46)(37,44)(41,52)(42,50)(43,51)(47,56)(48,54)(49,55)(53,58)(57,59);(30,38)(34,44)(39,50)(40,51)(45,54)(46,55)(52,58)(56,59)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4993);