Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #423×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3079 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #423×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #423 | D71 |
| hypocenter | C71 | #3079 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^70,f^c=fg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31893302, #31893304, #31893309, … |
| maximal normal subgroup of | #31893302, #31893304, #31893309, … |
| maximal quotient of | #31996948, #31998432, #31999638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 14326);