Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C192 ⋊ C3×C4 |
| Hall | C19⋊Dic95 ⋊ C3 |
| Hall | C5×#11762245 ⋊ C4 |
| Hall | #11762245 ⋊ Dic5 |
| Sylow | C192 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ #16864558 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#14524206 |
| commutator, hypocenter | C5×C192 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C192 | C2×C3 |
| prime radical | C2×C5×#11762245 | C2 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 ◁ C2 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7220 |
Polycyclic presentation:
2,3,5,19^2,2|a^2=f,c^a=c^4,d^a=d^18,e^a=e^18,d^b=d^7,e^b=e^7624 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 60);