Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1833 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556670 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | #97×C73 | C4 |
| socle | C2×C73 | #382 |
| hypercenter | #97 | #64408 |
| hypocenter | C73 | #1833 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C42 ◁ #97 | |
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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=f,b^2=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^27,f^b=fg,h^b=h^72,f^c=fg,h^f=h^72392 conjugacy classes — view the full character table.
| maximal subgroup of | #34013150, #34013151, #34013152, … |
| maximal normal subgroup of | #34013150, #34013151, #34013152, … |
| maximal quotient of | #34005411, #34005412, #34005415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20430);