Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #1840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D73 |
| commutator, socle | C23×C73 | C22×C4 |
| Fitting | #336×C73 | C2 |
| hypercenter | #336 | D73 |
| hypocenter | C73 | #1840 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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=de,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^721484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1840×D73, C2×#22610075, #33086235, … |
| maximal normal subgroup of | #1840×D73, C2×#22610075, #33086235, … |
| maximal quotient of | #32979709, #32979710, #32979711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4654);