Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #342×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556098 |
| commutator | C24×C71 | C23 |
| Frattini | C24 | C22×D71 |
| Fitting | #342×C71 | C2 |
| socle | C22×C71 | #120 |
| hypercenter | #342 | D71 |
| hypocenter | C71 | #2021 |
| LCS | G ▷ C24×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^a=bd,c^a=ce,f^a=fg,h^a=h^70,c^b=cf,h^b=h^70,d^c=dg,h^c=h^70796 conjugacy classes — view the full character table.
| maximal subgroup of | #31909482, #31909487, #31909500, … |
| maximal normal subgroup of | #31909482, #31909487, #31909500, … |
| maximal quotient of | #31897651, #31897658, #31897665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5637);