Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×D284 |
| Fitting | C43×C71 ⋊ C2 |
| Sylow | C71 ⋊ C42×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D71 |
| commutator | C2×C71 | C22×C42 |
| Frattini | C23 | C23×D71 |
| Fitting | C43×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C43 | D71 |
| hypocenter | C71 | C42×D4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C42 ◁ C43 | |
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 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.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#17985728, C4×#17985726, #31888055, … |
| maximal normal subgroup of | C4×#17985728, C4×#17985726, #31888055, … |
| maximal quotient of | C42×(C2×D71)⋊C4, C42×C4⋊Dic71, C4×#17985877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6858);