Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C71⋊C32) |
| Sylow | C71 ⋊ C4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D71 |
| commutator | C2×C71 | C2×C32 |
| Fitting | C4×C16×C71 | C2 |
| socle | C22×C71 | C2×C16 |
| hypercenter | C4×C16 | D71 |
| hypocenter | C71 | C4⋊C32 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C16 ◁ C4×C16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=c,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 | D4⋊(C71⋊C32), #31884891, #31884893, … |
| maximal normal subgroup of | D4⋊(C71⋊C32), #31884891, #31884893, … |
| maximal quotient of | #31885118, #31885125, #31885139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2706);