Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #64408 |
| commutator, hypocenter | C73 | C2×C64 |
| Frattini | C16 | C2×#64408 |
| Fitting | C32×C73 | C4 |
| socle | C2×C73 | C2×C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^27,h^b=h^72,h^c=h^72704 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#64408, #34001203, #34001268, … |
| maximal normal subgroup of | C64×#64408, #34001203, #34001268, … |
| maximal quotient of | #34001202, #34001211, #34001277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19678);