Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×C71⋊C8 |
| Sylow | C71 ⋊ C8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C2×C71 | C2×C4×C8 |
| Fitting | C4×C22⋊C4×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C4×C22⋊C4 | D71 |
| hypocenter | C71 | C8×C22⋊C4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #31887992, #99×C71⋊C8, #31888002, … |
| maximal normal subgroup of | #31887992, #99×C71⋊C8, #31888002, … |
| maximal quotient of | C22⋊C8×C71⋊C8, #31887927, #31887943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4283);