Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20935 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,27)(28,29,33,39,34,37,32,38)(30,40,44,35,42,50,43,51)(31,45,47,36,48,53,46,52)(41,49,57,54,55,59,56,58);(20,21,22,23)(28,30)(29,35)(31,41)(32,44)(33,43)(34,42)(36,49)(37,51)(38,50)(39,40)(45,54)(46,57)(47,56)(48,55)(52,59)(53,58);(25,27)(28,31,34,48)(29,36,37,52)(30,41,42,55)(32,47,33,46)(35,49,51,59)(38,53,39,45)(40,54,50,58)(43,57,44,56);(29,37)(30,42)(36,52)(38,39)(41,55)(43,44)(45,53)(56,57)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13923);