Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C73 ⋊ C4×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C4×M32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
196 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 118 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=d,b^2=e,d^2=f,f^2=g,c^a=cg,h^a=h^27,h^b=h^72,h^d=h^72656 conjugacy classes — view the full character table.
| maximal subgroup of | #34000151, #34000153, #34000155, … |
| maximal normal subgroup of | #34000151, #34000153, #34000155, … |
| maximal quotient of | C8×#14556665, #34009664, #34009713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20716);