Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#22949 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(21,24)(25,27)(28,29,33,37,34,38,32,46)(30,35,41,49,42,50,40,56)(31,43,45,36,44,52,47,51)(39,53,55,48,54,59,57,58);(20,21)(22,25)(23,24)(26,27)(28,30,33,41,34,42,32,40)(29,35,37,49,38,50,46,56)(31,39,45,55,44,54,47,57)(36,48,52,59,51,58,43,53);(20,22,23,26)(21,25,24,27)(28,31)(29,36)(30,39)(32,47)(33,45)(34,44)(35,48)(37,52)(38,51)(40,57)(41,55)(42,54)(43,46)(49,59)(50,58)(53,56);(21,24)(25,27)(31,44)(36,51)(39,54)(43,52)(45,47)(48,58)(53,59)(55,57)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15937);