Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×2−1+4×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3487 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | C2×2−1+4×C71 | C2 |
| hypercenter | C2×2−1+4 | D71 |
| hypocenter | C71 | #3487 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=f,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^701234 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31913012, #32006630, #32028880, … |
| maximal normal subgroup of | #31913012, #32006630, #32028880, … |
| maximal quotient of | #32157480, #32157742, #32158387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18165);