Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C127 · Schur multiplier (H2) = C2 |
| direct product | #360×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | #102 |
| commutator | C8 | C2×C4×C127 |
| Frattini, cosocle | C2×C8 | C22×C127 |
| prime radical | #135×C127 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×C8×C127 ◁ G | |
58 conjugacy classes of subgroups.
2032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#360×C127, C127×#2145, C127×#2180, … |
| maximal normal subgroup of | C2×#360×C127, C127×#2145, C127×#2180, … |
| maximal quotient of | C127×#1333, C127×#1334, C127×#1347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 41);