Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C139 · Schur multiplier (H2) = C23 |
| direct product | C4×D8×C139 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C139 | D4 |
| commutator | C4 | C22×C4×C139 |
| Frattini, cosocle | C2×C4 | C23×C139 |
| socle | C22×C139 | C2×D4 |
| prime radical | C2×D8×C139 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C139 ◁ C42×C139 ◁ G | |
134 conjugacy classes of subgroups.
3892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 118);