Finite Group DatabasebetaFinite Group Databasebeta| order | 15588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C4×C9 |
| Hall | #16838985 ⋊ C4 |
| Hall | Dic433 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D433⋊C3 |
| commutator, hypocenter | C433 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C433 | C2×C3 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15588 |
Polycyclic presentation:
2,3,433,2,3|a^2=d,b^3=e,c^a=c^432,c^b=c^198468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15588, 2);