Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#16813320 |
| unambiguous semidirect product | #14267798⋊C8 |
| Fitting | C4×C449 ⋊ C8 |
| derived, Sylow | C449 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16813320 |
| commutator, hypocenter | C449 | C4×C8 |
| Frattini | C2 | C2×#16813320 |
| Fitting | C4×C449 | C8 |
| socle | C2×C449 | C2×C8 |
| prime radical | C2×D449 | C2×C4 |
| cosocle | C2×#14267798 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1796 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#16813320, #43273091, D4⋊#16813320, … |
| maximal normal subgroup of | C8×#16813320, #43273091, D4⋊#16813320, … |
| maximal quotient of | C8×#16813320, #43273091, (C2×#16813320)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 237);