Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #338×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2091 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556588 |
| commutator | C22×C4×C73 | C23 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #338×C73 | C2 |
| socle | C2×C73 | #399 |
| hypercenter | #338 | D73 |
| hypocenter | C73 | #2091 |
| LCS | G ▷ C22×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #338 | |
222 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=de,d^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^72,h^c=h^72818 conjugacy classes — view the full character table.
| maximal subgroup of | #32999310, #32999315, #32999321, … |
| maximal normal subgroup of | #32999310, #32999315, #32999321, … |
| maximal quotient of | #32990954, #32990961, #32990966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6027);