Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C25 |
| direct product | C22×M16×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C127 | C22 |
| commutator | C2 | C23×C4×C127 |
| Frattini, cosocle | C4 | C24×C127 |
| socle | C23×C127 | C2×C4 |
| prime radical | C24×C127 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C127 ◁ G | |
298 conjugacy classes of subgroups.
5080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1728, C127×#1729, C2×H(3,ℤ/4)×C127, … |
| maximal normal subgroup of | C127×#1728, C127×#1729, C2×H(3,ℤ/4)×C127, … |
| maximal quotient of | C22×#97×C127, C2×C4×M16×C127, C22×C22⋊C8×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 247);