Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#17986058 |
| Fitting | C2×C4×C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#433 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C2×C4×C8×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×C4×C8 | D71 |
| hypocenter | C71 | C2×#433 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 | |
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31887989, #31887991, #31890318, … |
| maximal normal subgroup of | #31887989, #31887991, #31890318, … |
| maximal quotient of | C2×#22588091, C2×#22588107, C2×#22588198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13134);