Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #117×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C4×#64408 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | #117×C73 | C4 |
| socle | C2×C73 | C2×#95 |
| hypercenter | #117 | #64408 |
| hypocenter | C73 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ #117 | |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^27,e^b=eg,h^c=h^72,h^e=h^72404 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,ℤ/4)×#64408, #34008262, #34008408, … |
| maximal normal subgroup of | H(3,ℤ/4)×#64408, #34008262, #34008408, … |
| maximal quotient of | #34001974, #34001976, #34001978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20180);