Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #533×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2031 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556580 |
| commutator | C22×C4×C73 | C23 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #533×C73 | C2 |
| socle | C2×C73 | #393 |
| hypercenter | #533 | D73 |
| hypocenter | C73 | #2031 |
| LCS | G ▷ C22×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #533 | |
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^c=dg,e^c=eg,f^c=fg,h^c=h^721034 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2031×D73, C2×#22611100, #33113412, … |
| maximal normal subgroup of | #2031×D73, C2×#22611100, #33113412, … |
| maximal quotient of | #32989069, #32989074, #32989079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 5679);