Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D271 |
| Fitting | C16×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D271 |
| commutator, hypocenter | C271 | C2×C16 |
| Frattini | C8 | C2×D271 |
| Fitting | C16×C271 | C2 |
| socle | C2×C271 | C2×C8 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D271, #31773730, C2×C16×D271, … |
| maximal normal subgroup of | C32×D271, #31773730, C2×C16×D271, … |
| maximal quotient of | C16×Dic271, (C2×D271)⋊C16, Dic271⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 83);