Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C127 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D127 |
| commutator, socle | C2×C127 | C23×C4 |
| Fitting | C2×#41×C127 | C2 |
| hypercenter | C2×#41 | D127 |
| hypocenter | C127 | #568 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,e^2=f,d^a=df,g^a=g^126,c^b=cf1294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638949, #30638952, #30638968, … |
| maximal normal subgroup of | #30638949, #30638952, #30638968, … |
| maximal quotient of | #30647149, #30647158, #30647175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1316);