Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C449 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20297750 |
| commutator, hypocenter | C449 | C32 |
| Fitting, socle, prime radical | C2×C449 | C16 |
| cosocle | #20297748 | C2 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14368 |
Polycyclic presentation:
2^5,449|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^349,f^b=f^122,f^c=f^67,f^d=f^44888 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28385439, #43273136, #43273137, … |
| maximal normal subgroup of | C2×#28385439, #43273136, #43273137, … |
| maximal quotient of | #43273131, C2×#28385439 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 245);