Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21477 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C4×#120 |
| prime radical | C19×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,27,30,26,31,25,41)(22,32,35,28,36,45,42,46)(23,37,38,40,39,29,43,24)(33,47,49,44,50,34,48,51);(20,22)(21,28)(23,33)(24,34)(25,42)(26,36)(27,35)(29,44)(30,45)(31,46)(32,41)(37,51)(38,49)(39,50)(40,47)(43,48);(20,23)(21,29)(22,33)(24,30)(25,43)(26,39)(27,38)(28,44)(31,37)(32,47)(34,45)(35,49)(36,50)(40,41)(42,48)(46,51);(20,24,27,37,26,40,25,29)(21,23,30,38,31,39,41,43)(22,34,35,51,36,47,42,44)(28,33,45,49,46,50,32,48)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14465);