Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C127 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic127 |
| commutator | C4×C127 | C42 |
| Frattini | C2×C8 | C2×D127 |
| Fitting | M32×C127 | C2 |
| socle | C2×C127 | #97 |
| hypercenter | M32 | D127 |
| hypocenter | C127 | #347 |
| LCS | G ▷ C4×C127 ▷ C127 | |
| UCS | C1 ◁ C4 ◁ M32 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D127, C2×#22549653, #30640333, … |
| maximal normal subgroup of | #347×D127, C2×#22549653, #30640333, … |
| maximal quotient of | #30636650, #30636652, #30636809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 326);