Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #504×D71 |
| Fitting | #504×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C22×D71 |
| commutator, socle | C2×C71 | C23×C8 |
| Frattini | C8 | C23×D71 |
| Fitting | #504×C71 | C2 |
| hypercenter | #504 | D71 |
| hypocenter | C71 | C2×#504 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C16 ◁ #504 | |
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1401×D71, #31917661, #2170×D71, … |
| maximal normal subgroup of | #1401×D71, #31917661, #2170×D71, … |
| maximal quotient of | #2108×D71, #504×Dic71, #32150096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17607);