Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C449 ⋊ C2 |
| Sylow | C449 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|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 | #43272198, #123×D449, C2×#28385324, … |
| maximal normal subgroup of | #43272198, #123×D449, C2×#28385324, … |
| maximal quotient of | #43271868, #43271882, #43271884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 130);