Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×C22⋊D71 |
| Fitting | C22×C22⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C22×C22⋊C4×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C22×C22⋊C4 | D71 |
| hypocenter | C71 | D4×C22⋊C4 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
1252 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32012772, #99×C22⋊D71, #32013580, … |
| maximal normal subgroup of | #32012772, #99×C22⋊D71, #32013580, … |
| maximal quotient of | C22⋊C4×(C2×D71)⋊C4, C22⋊C4×C22⋊Dic71, C22⋊C4×Dic71⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7329);