Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×C4⋊C4×D71 |
| Fitting | C22×C4⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C23×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C2×C71 | C24×C4 |
| Frattini | C22 | C24×D71 |
| Fitting | C22×C4⋊C4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C4⋊C4 | D71 |
| hypocenter | C71 | C23×C4⋊C4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31888780, #31902718, #31902728, … |
| maximal normal subgroup of | #31888780, #31902718, #31902728, … |
| maximal quotient of | C22×#95×D71, C2×C4×C4⋊C4×D71, C22×#17985850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17669);