Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2360 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C22⋊Q8×C73 | C4 |
| hypercenter | C22⋊Q8 | #64408 |
| hypocenter | C73 | #2360 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^a=h^46,d^b=de,h^b=h^27,h^g=h^72302 conjugacy classes — view the full character table.
| maximal subgroup of | #34027700, #34027705, #34027708, … |
| maximal normal subgroup of | #34027700, #34027705, #34027708, … |
| maximal quotient of | #34014682, #34014709, #34014715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21034);