Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#17984887 |
| Fitting | C22×D4×C139 ⋊ C2 |
| Sylow | C139 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D139 |
| commutator | C2×C139 | C25 |
| Frattini | C2 | C24×D139 |
| Fitting | C22×D4×C139 | C2 |
| socle | C22×C139 | C24 |
| hypercenter | C22×D4 | D139 |
| hypocenter | C139 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31806350, #31806351, #31806357, … |
| maximal normal subgroup of | #31806350, #31806351, #31806357, … |
| maximal quotient of | C2×#22581425, C2×#22581426, C2×#22581428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1379);