Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C127 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | C4×Q8×C127 | C2 |
| hypercenter | C4×Q8 | D127 |
| hypocenter | C127 | #557 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^126,d^b=de1285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637825, #30637829, #30637887, … |
| maximal normal subgroup of | #30637825, #30637829, #30637887, … |
| maximal quotient of | Q8×C4⋊Dic127, #30641648, #30641685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1278);