Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C22⋊C8×C73 ⋊ C4 |
| Sylow | C73 ⋊ C8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C2×C4×C8 |
| Fitting | C22⋊C8×C73 | C4 |
| socle | C22×C73 | C2×C42 |
| hypercenter | C22⋊C8 | #64408 |
| hypocenter | C73 | C8×C22⋊C4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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,h^a=h^46,h^b=h^46,h^c=h^27,h^e=h^72,h^f=h^72440 conjugacy classes — view the full character table.
| maximal subgroup of | #34003463, #34003467, #34003479, … |
| maximal normal subgroup of | #34003463, #34003467, #34003479, … |
| maximal quotient of | C22⋊C8×#10596833, #34003383, #34003390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20245);