Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C61 ⋊ C4×C9 |
| Hall | #16838636 ⋊ C4 |
| Hall | C7×Dic61 ⋊ C9 |
| Hall | Dic61 ⋊ C7⋊C9 |
| Sylow | C61 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ Dic61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #14579420 |
| commutator, hypocenter | C7×C61 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C61 | C2×C3 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15372 |
Polycyclic presentation:
2,3,7,61,2,3|a^2=e,b^3=f,d^a=d^60,c^b=c^2,d^b=d^47480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 15);