Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #13181884 |
| commutator, hypocenter | C433 | C2×C16 |
| Frattini | C4 | C2×#13181884 |
| Fitting | C8×C433 | C4 |
| socle | C2×C433 | C2×C8 |
| prime radical | C2×D433 | C8 |
| cosocle | #16812358 | C22 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^5,433|a^2=c,c^2=d,d^2=e,f^a=f^179,f^b=f^432,f^c=f^432896 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#13181884, #42122698, #42122723, … |
| maximal normal subgroup of | C16×#13181884, #42122698, #42122723, … |
| maximal quotient of | #42122697, #42122706, #42122732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 219);