Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ C4⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator | C22×C73 | C2×C42 |
| Fitting | C2×C4⋊C4×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C4⋊C4 | #64408 |
| hypocenter | C73 | C4⋊#95 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
656 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^b=h^27,h^g=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | #34000315, #34008536, #34008537, … |
| maximal normal subgroup of | #34000315, #34008536, #34008537, … |
| maximal quotient of | (C2×#64408)⋊#95, #34001294, #34001295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19687);