Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#17985776 |
| Sylow | C71 ⋊ C2×#347 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic71 |
| commutator | C4×C71 | C2×C42 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | C2×M32×C71 | C2 |
| socle | C22×C71 | #97 |
| hypercenter | C2×M32 | D71 |
| hypocenter | C71 | C2×#347 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M32 | |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×Dic71, C4×#17985776, #31912281, … |
| maximal normal subgroup of | #347×Dic71, C4×#17985776, #31912281, … |
| maximal quotient of | C2×#22586260, C2×#22586262, #31906452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6111);