Finite Group DatabasebetaFinite Group Databasebeta| order | 15507 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C1723⋊C3 |
| unambiguous semidirect product | C1723⋊C32 |
| unambiguous semidirect product | (C3×C1723)⋊C3 |
| Fitting, socle | C3×C1723 ⋊ C3 |
| derived, Sylow | C1723 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C1723⋊C3 |
| commutator, cosocle, hypocenter | C1723 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1723 | C3 |
| LCS | G ▷ C1723 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5169 |
1731 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D1723⋊C3, C3⋊(D1723⋊C3), D3×C1723⋊C3, … |
| maximal normal subgroup of | C3×D1723⋊C3, C3⋊(D1723⋊C3), D3×C1723⋊C3, … |
| maximal quotient of | C2×C3×C1723⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15507, 3);