Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1305 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C71⋊#95 |
| commutator | C23×C71 | C42 |
| Frattini | C23×C4 | C2×D71 |
| Fitting | #380×C71 | C2 |
| socle | C22×C71 | #95 |
| hypercenter | #380 | D71 |
| hypocenter | C71 | #1305 |
| LCS | G ▷ C23×C71 ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #380 | |
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,b^2=e,d^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^70,c^b=cg,d^b=df1006 conjugacy classes — view the full character table.
| maximal subgroup of | #1305×D71, C2×#22586246, #31887784, … |
| maximal normal subgroup of | #1305×D71, C2×#22586246, #31887784, … |
| maximal quotient of | #31884023, #31884026, #31884027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2416);