Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10596842 |
| commutator | C2×C73 | C22×C16 |
| Fitting | C4⋊C4×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C4⋊C4 | #10596842 |
| hypocenter | C73 | D4×C16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
174 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,e^2=f,f^2=g,b^a=bd,h^a=h^63,h^b=h^72,h^c=h^10,h^e=h^27,h^f=h^72170 conjugacy classes — view the full character table.
| maximal subgroup of | #34033935, #34033936, #34033938, … |
| maximal normal subgroup of | #34033935, #34033936, #34033938, … |
| maximal quotient of | #34033936, #34033959, #34033974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21719);