Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #487×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3225 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #487×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #487 | D71 |
| hypocenter | C71 | #3225 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #487 | |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^70,c^b=ce,d^b=dg,f^c=fg,h^c=h^70,h^d=h^70796 conjugacy classes — view the full character table.
| maximal subgroup of | #3225×D71, C2×#22599452, #32868863, … |
| maximal normal subgroup of | #3225×D71, C2×#22599452, #32868863, … |
| maximal quotient of | #32006830, #32007222, #32008067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15622);