Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C127 ⋊ C2 |
| Sylow | C127 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D127 |
| commutator, socle | C2×C127 | C22×C8 |
| Fitting | M32×C127 | C2 |
| hypercenter | M32 | D127 |
| hypocenter | C127 | #504 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,d^2=e,e^2=f,g^a=g^126,c^b=cf,g^c=g^1261300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30640564, #30640566, #30640569, … |
| maximal normal subgroup of | #30640564, #30640566, #30640569, … |
| maximal quotient of | #30640328, #30640329, #30640342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 967);