Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C127 ⋊ #543 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | C2×C22⋊C4×C127 | C2 |
| hypercenter | C2×C22⋊C4 | D127 |
| hypocenter | C127 | #543 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
242 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637652, #30637655, #30637686, … |
| maximal normal subgroup of | #30637652, #30637655, #30637686, … |
| maximal quotient of | #30641342, #30641344, #30641458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1175);