Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#17986740 |
| Fitting | C2×#126×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#560 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×#126×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#126 | D71 |
| hypocenter | C71 | C2×#560 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1018 conjugacy classes — view the full character table.
| maximal subgroup of | #32160139, C4×#17986740, #32163256, … |
| maximal normal subgroup of | #32160139, C4×#17986740, #32163256, … |
| maximal quotient of | C2×#22591480, C2×#22591487, C2×#22591493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18628);