Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #407×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2974 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | #407×C71 | C2 |
| hypercenter | #407 | D71 |
| hypocenter | C71 | #2974 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,f^2=g,b^a=be,d^a=de,h^a=h^70,c^b=ceg,h^c=h^701030 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31963715, #31963718, #31963725, … |
| maximal normal subgroup of | #31963715, #31963718, #31963725, … |
| maximal quotient of | #31996137, #31996138, #31996195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13546);