Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×Dic139⋊C4 |
| Sylow | C139 ⋊ C22×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D139 |
| commutator | C2×C139 | C23×C4 |
| Frattini | C22 | C23×D139 |
| Fitting | C23×C4×C139 | C2 |
| socle | C24×C139 | C22 |
| hypercenter | C23×C4 | D139 |
| hypocenter | C139 | C22×C4⋊C4 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
418 conjugacy classes of subgroups.
2248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic139⋊#95, #31804635, #31804637, … |
| maximal normal subgroup of | Dic139⋊#95, #31804635, #31804637, … |
| maximal quotient of | C22×C139⋊#95, C2×C4×Dic139⋊C4, C2×#22580811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 999);