Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #456×D71 |
| Fitting | #456×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#456 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #456×C71 | C2 |
| socle | C2×C71 | C2×#120 |
| hypercenter | #456 | D71 |
| hypocenter | C71 | C2×#456 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #456 | |
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
592 conjugacy classes — view the full character table.
| maximal subgroup of | #1405×D71, #31917721, #2203×D71, … |
| maximal normal subgroup of | #1405×D71, #31917721, #2203×D71, … |
| maximal quotient of | #1603×D71, #1609×D71, #1604×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13849);