Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C127 · Schur multiplier (H2) = C23 |
| direct product | #408×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C23 |
| commutator | C22 | C22×C4×C127 |
| Frattini, cosocle | C2×C4 | C23×C127 |
| socle | C22×C127 | C22×C4 |
| prime radical | C2×#41×C127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ G | |
158 conjugacy classes of subgroups.
3556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1315, C127×#1321, C127×#1391, … |
| maximal normal subgroup of | C127×#1315, C127×#1321, C127×#1391, … |
| maximal quotient of | C127×#1468, C127×#1469, C127×#1470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 89);