Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #1791 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556560 |
| commutator | C23×C73 | C22×C4 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #585×C73 | C2 |
| socle | C2×C73 | #379 |
| hypercenter | #585 | D73 |
| hypocenter | C73 | #1791 |
| LCS | G ▷ C23×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #585 | |
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^72,e^b=eg,f^b=fg,d^c=dg1256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33003274, #33003275, #33003281, … |
| maximal normal subgroup of | #33003274, #33003275, #33003281, … |
| maximal quotient of | #32977377, #32977380, #32977505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4461);