Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C71⋊#1304 |
| Sylow | C71 ⋊ #1304 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C71⋊#95 |
| commutator | C23×C71 | C42 |
| Frattini | C25 | C2×D71 |
| Fitting | #379×C71 | C2 |
| socle | C22×C71 | #95 |
| hypercenter | #379 | D71 |
| hypocenter | C71 | #1304 |
| LCS | G ▷ C23×C71 ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ #379 | |
396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^701006 conjugacy classes — view the full character table.
| maximal subgroup of | #31884935, #31884936, #31885031, … |
| maximal normal subgroup of | #31884935, #31884936, #31885031, … |
| maximal quotient of | #31884022, #31884023, #31884029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2414);