Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C22 |
| direct product | #401×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C127 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C127 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ G | |
118 conjugacy classes of subgroups.
2794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#401×C127, C127×#2401, C127×#2493, … |
| maximal normal subgroup of | C2×#401×C127, C127×#2401, C127×#2493, … |
| maximal quotient of | C127×#1443, C127×#2104, C2×#401×C127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 82);