Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C449 ⋊ C2 |
| Sylow | C449 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D449 |
| commutator, socle | C2×C449 | C2×C8 |
| Fitting | C16×C449 | C2 |
| prime radical | C2×D449 | C8 |
| cosocle | C8×C449 | C22 |
| hypercenter | C16 | D449 |
| hypocenter | C449 | M32 |
| LCS | G ▷ C2×C449 ▷ C449 | |
| UCS | C1 ◁ C8 ◁ C16 | |
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^b=f^4483604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M32×D449, C2×#28385279, #43272423, … |
| maximal normal subgroup of | M32×D449, C2×#28385279, #43272423, … |
| maximal quotient of | #43271782, #43271786, #43271825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 85);