Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C2×C42 |
| Fitting | C2×M16×C73 | C4 |
| hypercenter | C2×M16 | #64408 |
| hypocenter | C73 | #1729 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=e,b^2=f,e^2=g,b^a=bd,h^a=h^46,c^b=cg,h^b=h^27,h^e=h^72,h^f=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | #34000324, #34000330, #34008433, … |
| maximal normal subgroup of | #34000324, #34000330, #34008433, … |
| maximal quotient of | #34001955, #34001956, #34001963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20178);