Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×C22⋊D71 |
| Fitting | C22×C16×C71 ⋊ C2 |
| Sylow | C71 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D71 |
| commutator | C2×C71 | C22×C16 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | C22×C16×C71 | C2 |
| socle | C22×C71 | C22×C8 |
| hypercenter | C22×C16 | D71 |
| hypocenter | C71 | D4×C16 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C16 ◁ C22×C16 | |
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C22⋊D71)⋊C32, C32×C22⋊D71, #31918001, … |
| maximal normal subgroup of | (C22⋊D71)⋊C32, C32×C22⋊D71, #31918001, … |
| maximal quotient of | C16×#11765850, C16×#11765853, C16×#11765852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6328);