Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D127 |
| Fitting | C32×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D127 |
| commutator, hypocenter | C127 | C2×C32 |
| Frattini | C16 | C2×D127 |
| Fitting | C32×C127 | C2 |
| socle | C2×C127 | C2×C16 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D127, #30636940, C2×C32×D127, … |
| maximal normal subgroup of | C64×D127, #30636940, C2×C32×D127, … |
| maximal quotient of | C32×Dic127, (C2×D127)⋊C32, Dic127⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 380);