Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C127 · Schur multiplier (H2) = C25 |
| direct product | C22×SD16×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | D4 |
| commutator, Frattini, cosocle | C4 | C24×C127 |
| prime radical | C22×D4×C127 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C22×C4×C127 ◁ G | |
298 conjugacy classes of subgroups.
3556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1877, C127×#1880, C127×#1968, … |
| maximal normal subgroup of | C127×#1877, C127×#1880, C127×#1968, … |
| maximal quotient of | C22×#102×C127, C22×#103×C127, C22×#106×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 251);