Finite Group DatabasebetaFinite Group Databasebeta| order | 15450 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C103 · Schur multiplier (H2) = C5 |
| direct product | C103×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C5⋊D5×C103) |
| unambiguous semidirect product | C5⋊(D15×C103) |
| Fitting, socle, Hall | C3×C52×C103 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C2×C103 |
| Hall | C52×C103 ⋊ D3 |
| Hall | C3×C103 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D3×C103 |
| Sylow | C3 ⋊ C5⋊D5×C103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C103 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C103 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C103 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C103 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7725 |
4017 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D15×C103, D515⋊D15, C3⋊(C5⋊D5)×D103, … |
| maximal normal subgroup of | D5×D15×C103, D515⋊D15, C3⋊(C5⋊D5)×D103, … |
| maximal quotient of | C103×C3⋊#1039, C2×C103×C3⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15450, 31);