Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×(C2×D71)⋊C4 |
| Fitting | C2×C4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ Q8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C2×C4×Q8×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×C4×Q8 | D71 |
| hypocenter | C71 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32013165, #32013166, #32013195, … |
| maximal normal subgroup of | #32013165, #32013166, #32013195, … |
| maximal quotient of | C4⋊C4×(C2×D71)⋊C4, Q8×C71⋊#95, #31918993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7343);