Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C449 ⋊ C2 |
| Sylow | C449 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D449 |
| commutator, socle, cosocle | C22×C449 | C23 |
| Fitting | C4⋊C4×C449 | C2 |
| prime radical | C22×D449 | C22 |
| hypercenter | C4⋊C4 | D449 |
| hypocenter | C449 | #126 |
| LCS | G ▷ C22×C449 ▷ C449 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^448,f^c=f^4482254 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D449, C2×#28385335, #43272534, … |
| maximal normal subgroup of | #126×D449, C2×#28385335, #43272534, … |
| maximal quotient of | #43271874, #43271888, #43271890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 141);