Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C509 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #14523266 |
| commutator, hypocenter | C509 | C16 |
| Fitting | C4×C509 | C4 |
| socle | C2×C509 | C8 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,509|a^2=b,b^2=c,c^2=d,e^a=e^301,e^b=e^508524 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22550864, D509⋊C16, #30654289, … |
| maximal normal subgroup of | C2×#22550864, D509⋊C16, #30654289, … |
| maximal quotient of | #30654265, C2×#22550864 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 43);