Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C127 ⋊ #342 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|a^2=d,b^2=e,b^a=bc,c^a=cf,d^b=df,g^b=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #342×D127, C2×#22549642, #30638461, … |
| maximal normal subgroup of | #342×D127, C2×#22549642, #30638461, … |
| maximal quotient of | #30636572, #30636576, #30636578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 315);