Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic139 |
| derived, Sylow | C139 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D139 |
| commutator, hypocenter | C139 | C24×C4 |
| Frattini | C2 | C24×D139 |
| Fitting, socle | C25×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
2272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804626, C22×C139⋊#95, C2×C22⋊C4×Dic139, … |
| maximal normal subgroup of | #31804626, C22×C139⋊#95, C2×C22⋊C4×Dic139, … |
| maximal quotient of | C23×C4×Dic139, C23×C22⋊Dic139, C23×C4⋊Dic139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1368);