Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#131×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2931 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C2×#131×C71 | C2 |
| hypercenter | C2×#131 | D71 |
| hypocenter | C71 | #2931 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,d^b=dg,h^b=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31906760, #31912647, #31913474, … |
| maximal normal subgroup of | #31906760, #31912647, #31913474, … |
| maximal quotient of | #31967966, #31967973, #31967975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13220);