Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C71⋊C32) |
| Sylow | C71 ⋊ C22⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D71 |
| commutator | C2×C71 | C2×C32 |
| Fitting | C22×C16×C71 | C2 |
| socle | C22×C71 | C2×C16 |
| hypercenter | C22×C16 | D71 |
| hypocenter | C71 | C22⋊C32 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C16 ◁ C22×C16 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^702320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884790, #31884791, #31884792, … |
| maximal normal subgroup of | #31884790, #31884791, #31884792, … |
| maximal quotient of | #31884791, #31884851, D4⋊(C71⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2648);