Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C127 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator | C2×C127 | C23×C4 |
| Fitting | C22×Q8×C127 | C2 |
| socle | C22×C127 | C24 |
| hypercenter | C22×Q8 | D127 |
| hypocenter | C127 | #519 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,g^a=g^126,c^b=ce1294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638842, #30638944, #30638947, … |
| maximal normal subgroup of | #30638842, #30638944, #30638947, … |
| maximal quotient of | #30641087, #30641095, #30641316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1027);