Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C22 |
| direct product | #510×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C23×C127 |
| prime radical | #135×C127 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×C8×C127 ◁ G | |
82 conjugacy classes of subgroups.
2032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#2180, C127×#2191, C127×#2194, … |
| maximal normal subgroup of | C127×#2180, C127×#2191, C127×#2194, … |
| maximal quotient of | C127×#2139, C127×#2141, C127×#2159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 191);