Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D271 |
| Fitting | D8×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D271 |
| commutator | C4×C271 | C23 |
| Frattini | C4 | C22×D271 |
| Fitting | D8×C271 | C2 |
| socle | C2×C271 | C2×D4 |
| hypercenter | D8 | D271 |
| hypocenter | C271 | C2×D8 |
| LCS | G ▷ C4×C271 ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
76 conjugacy classes of subgroups.
959 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D271, SD32×D271, #31774331, … |
| maximal normal subgroup of | D16×D271, SD32×D271, #31774331, … |
| maximal quotient of | #102×D271, #107×D271, #31773977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 155);