Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1955 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C22×C4 |
| Fitting | C2×C22⋊C8×C71 | C2 |
| hypercenter | C2×C22⋊C8 | D71 |
| hypocenter | C71 | #1955 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=f,b^2=df,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1955×D71, C2×#22589136, #32001043, … |
| maximal normal subgroup of | #1955×D71, C2×#22589136, #32001043, … |
| maximal quotient of | #31896248, #31896252, #31896256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5306);