Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×C22⋊D71 |
| Fitting | C22×#41×C71 ⋊ C2 |
| Sylow | C71 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C22×#41×C71 | C2 |
| hypercenter | C22×#41 | D71 |
| hypocenter | C71 | D4×#41 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
1648 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32013119, #104×C22⋊D71, #32013130, … |
| maximal normal subgroup of | #32013119, #104×C22⋊D71, #32013130, … |
| maximal quotient of | #41×(C2×D71)⋊C4, #41×C22⋊Dic71, #41×Dic71⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17995);