Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C271 ⋊ C2 |
| Sylow | C271 ⋊ #100 |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^2701361 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D271, C2×#22576076, #31773879, … |
| maximal normal subgroup of | #100×D271, C2×#22576076, #31773879, … |
| maximal quotient of | #31773620, #31773636, #31773640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 62);