Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #1939 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C22×C71 | C22×C8 |
| Fitting | C4×C4⋊C4×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C4×C4⋊C4 | D71 |
| hypocenter | C71 | #1939 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
260 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^70,h^b=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31891364, #31891365, #31891371, … |
| maximal normal subgroup of | #31891364, #31891365, #31891371, … |
| maximal quotient of | #31895990, #31895995, #31896000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5229);