Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#17985957 |
| Sylow | C71 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C2×C71 | C22×C42 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C22×M16×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C22×M16 | D71 |
| hypocenter | C71 | C2×#405 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
592 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31902620, #31902622, #31902643, … |
| maximal normal subgroup of | #31902620, #31902622, #31902643, … |
| maximal quotient of | C2×M16×C71⋊C8, C2×#22586624, C2×#22586627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 12925);