Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#17985905 |
| Sylow | C71 ⋊ C2×#391 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C23 | C23×D71 |
| Fitting | C22×C42×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C42 | D71 |
| hypocenter | C71 | C2×#391 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 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 | C2×#22586165, #31885449, #31885451, … |
| maximal normal subgroup of | C2×#22586165, #31885449, #31885451, … |
| maximal quotient of | C2×#22586570, C2×#22586573, C4×#17985905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6979);