Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×C71⋊C16 |
| Sylow | C71 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D71 |
| commutator | C2×C71 | C22×C16 |
| Fitting | C8×Q8×C71 | C2 |
| socle | C22×C71 | C22×C8 |
| hypercenter | C8×Q8 | D71 |
| hypocenter | C71 | Q8×C16 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
134 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31909215, SD16×C71⋊C16, #31909229, … |
| maximal normal subgroup of | #31909215, SD16×C71⋊C16, #31909229, … |
| maximal quotient of | C4⋊C4×C71⋊C16, #31915069, #31915453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6414);