Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C449 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16813320 |
| commutator, hypocenter | C449 | C2×C16 |
| Frattini | C2 | C2×#16813320 |
| Fitting | C4×C449 | C8 |
| socle | C2×C449 | C2×C8 |
| prime radical | C2×D449 | C8 |
| cosocle | #16813318 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|a^2=c,c^2=d,d^2=e,f^a=f^122,f^b=f^448,f^c=f^67,f^d=f^448256 conjugacy classes — view the full character table.
| maximal subgroup of | #43273100, #43273102, #43273107, … |
| maximal normal subgroup of | #43273100, #43273102, #43273107, … |
| maximal quotient of | C4×#20297748, #43273104, #43273110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 241);