Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C127⋊C16 |
| derived, Sylow | C127 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D127 |
| commutator, hypocenter | C127 | C4×C16 |
| Frattini | C2×C8 | C2×D127 |
| Fitting | C4×C8×C127 | C2 |
| socle | C22×C127 | C2×C8 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C127⋊C8, C8×C127⋊C16, #30636646, … |
| maximal normal subgroup of | C16×C127⋊C8, C8×C127⋊C16, #30636646, … |
| maximal quotient of | C8×C127⋊C16, #30636648, #30636808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 323);