Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C8×D127 |
| Fitting | C4×C8×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D127 |
| commutator, hypocenter | C127 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D127 |
| Fitting | C4×C8×C127 | C2 |
| socle | C22×C127 | C22×C4 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C4×C8 | |
162 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×D127, #322×D127, C8×#14523231, … |
| maximal normal subgroup of | C82×D127, #322×D127, C8×#14523231, … |
| maximal quotient of | C82×D127, #322×D127, C8×#14523231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 493);