Finite Group DatabasebetaFinite Group Databasebeta| order | 9423 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C349 ⋊ C3 |
| Sylow | C349 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C349⋊C3 |
| commutator, socle | C3×C349 | C32 |
| Fitting | C9×C349 | C3 |
| hypercenter | C9 | C349⋊C3 |
| hypocenter | C349 | 3−1+2 |
| LCS | G ▷ C3×C349 ▷ C349 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,349|a^3=c,b^a=bc,d^b=d^1221055 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 3−1+2×C349⋊C3, C3×#22628002, #43246524, … |
| maximal normal subgroup of | 3−1+2×C349⋊C3, C3×#22628002, #43246524, … |
| maximal quotient of | (C3×C349⋊C3)⋊C9, (C349⋊C9)⋊C9, #43246498, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9423, 11);