Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C73 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic73 |
| commutator | C4×C73 | C4×C8 |
| Frattini | C4×C8 | C2×D73 |
| Fitting | #322×C73 | C2 |
| socle | C22×C73 | #97 |
| hypercenter | #322 | D73 |
| hypocenter | C73 | #1313 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #322 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^72,c^b=cg1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1313×D73, C2×#22607852, #32994983, … |
| maximal normal subgroup of | #1313×D73, C2×#22607852, #32994983, … |
| maximal quotient of | #32972601, #32972814, #32973320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 2431);