Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #1768 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator | C22×C73 | C2×C42 |
| Fitting | #95×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | #95 | #64408 |
| hypocenter | C73 | #1768 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #95 | |
260 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^a=cg,h^b=h^27,h^f=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22625719, #34020152, C4×#17989593, … |
| maximal normal subgroup of | C2×#22625719, #34020152, C4×#17989593, … |
| maximal quotient of | #34003940, #34003943, #34003946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20298);