Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C22 | C23×#64408 |
| Fitting | #117×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | #117 | #64408 |
| hypocenter | C73 | C8×#41 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^46,h^c=h^27,h^f=h^72440 conjugacy classes — view the full character table.
| maximal subgroup of | #34003594, #34003600, #34003606, … |
| maximal normal subgroup of | #34003594, #34003600, #34003606, … |
| maximal quotient of | #117×#10596833, #34020335, C4×#17989614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21314);