Finite Group DatabasebetaFinite Group Databasebeta| order | 15450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C2×C52⋊(C103⋊C3) |
| unambiguous semidirect product | (C2×C52)⋊(C103⋊C3) |
| unambiguous semidirect product | (C2×C103)⋊(C52⋊C3) |
| Fitting, socle, Hall | C2×C52×C103 ⋊ C3 |
| derived, Hall | C52×C103 ⋊ C2×C3 |
| Hall | C2×C103 ⋊ C52⋊C3 |
| Sylow | C103 ⋊ C2×C52⋊C3 |
| Hall | C2×C52 ⋊ C103⋊C3 |
| Sylow | C52 ⋊ C2×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊(C103⋊C3) |
| commutator, cosocle, hypocenter | C52×C103 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C103 | C3 |
| LCS | G ▷ C52×C103 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3090 |
1722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44525444, #1039⋊(C103⋊C3), Dic103⋊(C52⋊C3), … |
| maximal normal subgroup of | #44525444, #1039⋊(C103⋊C3), Dic103⋊(C52⋊C3), … |
| maximal quotient of | C4×C52⋊(C103⋊C3), C22×C52⋊(C103⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15450, 27);