Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×(C2×D127)⋊C4 |
| Fitting | C23×C4×C127 ⋊ C2 |
| Sylow | C127 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D127 |
| commutator | C2×C127 | C23×C4 |
| Frattini | C22 | C23×D127 |
| Fitting | C23×C4×C127 | C2 |
| socle | C24×C127 | C22 |
| hypercenter | C23×C4 | D127 |
| hypocenter | C127 | C22×C22⋊C4 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
674 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D127)⋊#95, #30636966, #30636968, … |
| maximal normal subgroup of | (C2×D127)⋊#95, #30636966, #30636968, … |
| maximal quotient of | C22×C127⋊#95, C2×C4×(C2×D127)⋊C4, C2×#22549731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 996);