Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D127 |
| unambiguous semidirect product | C127⋊C26 |
| unambiguous semidirect product | (C2×C127)⋊C25 |
| Fitting, socle | C25×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D127 |
| commutator, hypocenter | C127 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C127 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #379×D127, C2×#22549731, #30647006, … |
| maximal normal subgroup of | #379×D127, C2×#22549731, #30647006, … |
| maximal quotient of | C24×C4×D127, C25×Dic127, C23×D4×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1387);