Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C449 ⋊ C2 |
| Sylow | C449 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|a^2=d,d^2=e,b^a=bc,f^b=f^4483604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D449, C2×#28385252, #43271969, … |
| maximal normal subgroup of | C22⋊C8×D449, C2×#28385252, #43271969, … |
| maximal quotient of | #43271730, #43271732, #43271734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 58);