Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16864637 |
| Fitting | C2×C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D271 |
| commutator | C2×C271 | C22×C4 |
| Frattini | C4 | C22×D271 |
| Fitting | C2×C8×C271 | C2 |
| socle | C22×C271 | C2×C4 |
| hypercenter | C2×C8 | D271 |
| hypocenter | C271 | C2×M16 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
68 conjugacy classes of subgroups.
2180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31773678, C4×#16864637, #31773849, … |
| maximal normal subgroup of | #31773678, C4×#16864637, #31773849, … |
| maximal quotient of | C2×#22576070, C4×#16864637, C2×(C2×D271)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 150);