Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D509 |
| Fitting | D4×C509 ⋊ C2 |
| Sylow | C509 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D509 |
| commutator, socle | C2×C509 | C23 |
| Fitting | D4×C509 | C2 |
| hypercenter | D4 | D509 |
| hypocenter | C509 | C2×D4 |
| LCS | G ▷ C2×C509 ▷ C509 | |
| UCS | C1 ◁ C2 ◁ D4 | |
54 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D509, SD16×D509, #30654239, … |
| maximal normal subgroup of | D8×D509, SD16×D509, #30654239, … |
| maximal quotient of | C22⋊C4×D509, C4⋊C4×D509, #30654175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 34);