Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C71⋊#1273 |
| Sylow | C71 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D71 |
| commutator | C2×C71 | C82 |
| Fitting | C2×C4×C8×C71 | C2 |
| socle | C23×C71 | C42 |
| hypercenter | C2×C4×C8 | D71 |
| hypocenter | C71 | #1273 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^702320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884224, #31884225, #31884237, … |
| maximal normal subgroup of | #31884224, #31884225, #31884237, … |
| maximal quotient of | C71⋊#7014, #31883979, #31883980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2337);