Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C127 · Schur multiplier (H2) = C24 |
| direct product | C2×#125×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C127 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C127 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ G | |
226 conjugacy classes of subgroups.
3556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1470, C2×#330×C127, C127×#1528, … |
| maximal normal subgroup of | C127×#1470, C2×#330×C127, C127×#1528, … |
| maximal quotient of | C2×#382×C127, C2×#387×C127, C2×#389×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 208);