Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C127 ⋊ C2 |
| Sylow | C127 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,g^a=g^126,e^b=ef,g^b=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30639091, #30639093, #30639230, … |
| maximal normal subgroup of | #30639091, #30639093, #30639230, … |
| maximal quotient of | #30647250, #30647320, #30647532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1349);