Finite Group DatabasebetaFinite Group Databasebeta| order | 9423 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C349 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C349⋊C3 |
| commutator, socle | C3×C349 | C32 |
| Fitting | C32×C349 | C3 |
| hypercenter | C32 | C349⋊C3 |
| hypocenter | C349 | 3−1+2 |
| LCS | G ▷ C3×C349 ▷ C349 | |
| UCS | C1 ◁ C3 ◁ C32 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,349|a^3=c,b^a=bc,d^a=d^2261055 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43246505, #43246506, #43246507, … |
| maximal normal subgroup of | #43246505, #43246506, #43246507, … |
| maximal quotient of | C32⋊(C349⋊C9), (C349⋊C9)⋊C9, C3×#22628003 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9423, 12);