Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C127 · Schur multiplier (H2) = C22 |
| direct product | C8×Q8×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C127 | C22 |
| commutator | C2 | C22×C8×C127 |
| Frattini, cosocle | C2×C4 | C23×C127 |
| socle, prime radical | C22×C127 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C127 ◁ G | |
102 conjugacy classes of subgroups.
5080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×Q8⋊C16, C8×SD16×C127, C8×Q16×C127, … |
| maximal normal subgroup of | C127×Q8⋊C16, C8×SD16×C127, C8×Q16×C127, … |
| maximal quotient of | C8×C4⋊C4×C127, C127×#1916, C127×#1939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 126);