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 | #97×C127 | C2 |
| socle | C2×C127 | #97 |
| hypercenter | #97 | D127 |
| hypocenter | C127 | #347 |
| LCS | G ▷ C4×C127 ▷ C127 | |
| UCS | C1 ◁ C4 ◁ #97 | |
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,g^a=g^126,c^b=cf1282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636762, #30636763, #30636764, … |
| maximal normal subgroup of | #30636762, #30636763, #30636764, … |
| maximal quotient of | #30636651, #30636810, C2×#22549654 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 327);