Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C127 · Schur multiplier (H2) = C22 |
| direct product | #343×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | C22⋊C4 |
| commutator | C22 | C42×C127 |
| Frattini, cosocle | C22×C4 | C22×C127 |
| prime radical | C23×C127 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C22×C4×C127 ◁ G | |
98 conjugacy classes of subgroups.
2794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#1345, C127×#1346, C127×#1353, … |
| maximal normal subgroup of | C127×#1345, C127×#1346, C127×#1353, … |
| maximal quotient of | C127×#1280, C127×#1283, C127×#1285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 24);