Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D509 |
| Fitting | C2×C4×C509 ⋊ C2 |
| derived, Sylow | C509 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D509 |
| commutator, hypocenter | C509 | C22×C4 |
| Frattini | C2 | C22×D509 |
| Fitting | C2×C4×C509 | C2 |
| socle | C22×C509 | C22 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30654127, C42×D509, C22⋊C4×D509, … |
| maximal normal subgroup of | #30654127, C42×D509, C22⋊C4×D509, … |
| maximal quotient of | C42×D509, C2×C4×Dic509, C22⋊C4×D509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 32);