Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C127 · Schur multiplier (H2) = C29 |
| direct product | C2×2−1+4×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | C24 |
| commutator, Frattini, cosocle | C2 | C25×C127 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ G | |
794 conjugacy classes of subgroups.
4318 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1793, C127×#1796, C127×#2884, … |
| maximal normal subgroup of | C127×#1793, C127×#1796, C127×#2884, … |
| maximal quotient of | C2×#519×C127, C2×#520×C127, C4×2−1+4×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 265);