Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C127⋊C8 |
| derived, Sylow | C127 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D127 |
| commutator, hypocenter | C127 | C23×C8 |
| Frattini | C4 | C23×D127 |
| Fitting | C23×C4×C127 | C2 |
| socle | C24×C127 | C4 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C23×C4 | |
338 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22549630, C2×#22549631, #30638427, … |
| maximal normal subgroup of | C2×#22549630, C2×#22549631, #30638427, … |
| maximal quotient of | C22×C4×C127⋊C8, C22×C22⋊(C127⋊C8), C22×C4⋊(C127⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1306);