Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C271 ⋊ C2 |
| Sylow | C271 ⋊ #102 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|a^2=d,c^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^2701364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D271, C2×#22576080, #31773891, … |
| maximal normal subgroup of | #102×D271, C2×#22576080, #31773891, … |
| maximal quotient of | #31773624, #31773630, #31773640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 66);