Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #460 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^126,e^c=ef,g^c=g^1261279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637790, #30637791, #30637796, … |
| maximal normal subgroup of | #30637790, #30637791, #30637796, … |
| maximal quotient of | #30638079, #30638091, #30638101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 750);