Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C73 ⋊ #2164 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C22⋊C4×C73 | C8 |
| hypercenter | C22⋊C4 | #10596842 |
| hypocenter | C73 | #2164 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 57 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,c^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^10,c^b=cg,h^e=h^27,h^f=h^72146 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22627136, #34034757, #34034763, … |
| maximal normal subgroup of | C2×#22627136, #34034757, #34034763, … |
| maximal quotient of | #34034076, #34034087, #34034125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21715);