Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C73 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#64408 |
| commutator | C4×C73 | C4×C8 |
| Frattini | C2×C8 | C2×#64408 |
| Fitting | C2×C16×C73 | C4 |
| socle | C22×C73 | #97 |
| hypercenter | C2×C16 | #64408 |
| hypocenter | C73 | #1313 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C16 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^46,c^b=cg,h^b=h^27,h^c=h^72,h^d=h^72620 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624850, #34009675, #34009681, … |
| maximal normal subgroup of | C2×#22624850, #34009675, #34009681, … |
| maximal quotient of | #33999982, #34000149, #34000765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19429);