Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#14556116 |
| Fitting | C22×C42×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C22×C42×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C42 | D71 |
| hypocenter | C71 | C22×#124 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31888802, #31888918, #31903994, … |
| maximal normal subgroup of | #31888802, #31888918, #31903994, … |
| maximal quotient of | C22×#17985865, C22×#17985890, C22×#17985901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17758);