Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C271 ⋊ C2 |
| Sylow | C271 ⋊ #104 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D1084 |
| commutator | C4×C271 | C2×C4 |
| Frattini | C2×C4 | C2×D271 |
| Fitting | C42×C271 | C2 |
| socle | C2×C271 | C22⋊C4 |
| hypercenter | C42 | D271 |
| hypocenter | C271 | #104 |
| LCS | G ▷ C4×C271 ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C42 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^270,c^b=ce,f^b=f^2702174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D271, C2×#22576088, #31773912, … |
| maximal normal subgroup of | #104×D271, C2×#22576088, #31773912, … |
| maximal quotient of | #31773626, #31773629, #31773630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 74);