Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#16813318 |
| derived, Sylow | C449 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14267798 |
| commutator, hypocenter | C449 | C4×C8 |
| Frattini | C22 | C2×#14267798 |
| Fitting | C2×C4×C449 | C4 |
| socle, prime radical | C22×C449 | C2×C4 |
| cosocle | C2×Dic449 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14368 |
928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16813318, #43272848, #43272849, … |
| maximal normal subgroup of | C8×#16813318, #43272848, #43272849, … |
| maximal quotient of | C8×#16813318, #43272848, #43272873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 199);