Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #423×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2925 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #423×C73 | C2 |
| hypercenter | #423 | D73 |
| hypocenter | C73 | #2925 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #423 | |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^72,d^b=dg,h^b=h^72,d^c=dg,h^c=h^721058 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32980288, #32980292, #32980302, … |
| maximal normal subgroup of | #32980288, #32980292, #32980302, … |
| maximal quotient of | #33083484, #33083538, #33083909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13178);