Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×#13095200 |
| derived, Sylow | C132 ⋊ C2×C5×C9 |
| Hall | C2×C5×C132 ⋊ C9 |
| Hall | C5×C132 ⋊ C2×C9 |
| Hall | C2×C132 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | #92788 |
| commutator, hypocenter | C132 | C2×C5×C9 |
| Frattini | C3 | C2×C5×#92788 |
| Fitting, socle, prime radical | C2×C3×C5×C132 | C3 |
| cosocle | C3×C132 | C2×C3×C5 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C3×C5 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15210 |
1770 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20258752, C5×#20258754, #44477588, … |
| maximal normal subgroup of | C5×#20258752, C5×#20258754, #44477588, … |
| maximal quotient of | C4×C5×#13095200, C22×C5×#13095200 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 54);