Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #336×C73 ⋊ C2 |
| Sylow | C73 ⋊ #1752 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D73 |
| commutator | C22×C73 | C2×C42 |
| Fitting | #336×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | #336 | D73 |
| hypocenter | C73 | #1752 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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=e,e^2=g,b^a=bd,c^b=cg,h^c=h^721496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1752×D73, C2×#22609706, #33083580, … |
| maximal normal subgroup of | #1752×D73, C2×#22609706, #33083580, … |
| maximal quotient of | #32976452, #32976456, #32976478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4285);