Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×C127⋊#95 |
| unambiguous semidirect product | (C2×C127)⋊#95 |
| Sylow | C127 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D127 |
| commutator | C2×C127 | C2×C42 |
| Frattini | C23 | C22×D127 |
| Fitting | C23×C4×C127 | C2 |
| socle | C24×C127 | C22 |
| hypercenter | C23×C4 | D127 |
| hypocenter | C127 | C2×#95 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
330 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636572, #30636608, #30636610, … |
| maximal normal subgroup of | #30636572, #30636608, #30636610, … |
| maximal quotient of | C4×C127⋊#95, #30636952, #30636953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 393);