Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C449 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16813320 |
| commutator, socle | C2×C449 | C2×C8 |
| Fitting, prime radical | C22×C449 | C8 |
| cosocle | #16813318 | C22 |
| hypercenter | C22 | #16813320 |
| hypocenter | C449 | M32 |
| LCS | G ▷ C2×C449 ▷ C449 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^122,f^c=f^67,f^d=f^448244 conjugacy classes — view the full character table.
| maximal subgroup of | #43273105, #43273106, C2×#28385436, … |
| maximal normal subgroup of | #43273105, #43273106, C2×#28385436, … |
| maximal quotient of | #43273101, C22⋊#20297748, #43273110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 242);