Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C73 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator | C2×C73 | C43 |
| Fitting | #95×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | #95 | #64408 |
| hypocenter | C73 | #1726 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #95 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^27,c^b=cg,h^d=h^72440 conjugacy classes — view the full character table.
| maximal subgroup of | #34003848, #34003852, #34003864, … |
| maximal normal subgroup of | #34003848, #34003852, #34003864, … |
| maximal quotient of | #34001929, #34001932, #34001938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20167);