Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #2171 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#10596842 |
| commutator | C4×C73 | C22×C8 |
| Frattini | C4 | C22×#10596842 |
| Fitting | Q16×C73 | C8 |
| socle | C2×C73 | C8×D4 |
| hypercenter | Q16 | #10596842 |
| hypocenter | C73 | #2171 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^a=dg,h^a=h^10,d^b=dg,h^b=h^72,h^c=h^10,h^e=h^27,h^f=h^72107 conjugacy classes — view the full character table.
| maximal subgroup of | #34034024, #34034025, #34034026, … |
| maximal normal subgroup of | #34034024, #34034025, #34034026, … |
| maximal quotient of | #34033938, #34033962, #34033964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21731);