Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #2072 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D73 |
| commutator | C22×C4×C73 | C23 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #340×C73 | C2 |
| socle | C23×C73 | C2×D4 |
| hypercenter | #340 | D73 |
| hypocenter | C73 | #2072 |
| LCS | G ▷ C22×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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=g,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^72,c^b=cf,f^b=fg,h^b=h^72,f^c=fg1040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2072×D73, C2×#22611343, #33114742, … |
| maximal normal subgroup of | #2072×D73, C2×#22611343, #33114742, … |
| maximal quotient of | #32990698, #32990703, #32990716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 5922);