Finite Group DatabasebetaFinite Group Databasebeta| order | 15723 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1747 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C1747⋊C3 |
| commutator, hypocenter | C1747 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C1747 | C3 |
| LCS | G ▷ C1747 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15723 |
Polycyclic presentation:
3^2,1747|a^3=b,c^a=c^3711755 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30628420⋊C2, C2×#30628420 |
| maximal normal subgroup of | #30628420⋊C2, C2×#30628420 |
| maximal quotient of | C2×#30628420 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15723, 1);