Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#20297739 |
| derived, Sylow | C449 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14267798 |
| commutator, hypocenter | C449 | C2×C16 |
| Frattini | C4 | C2×#14267798 |
| Fitting | C2×C4×C449 | C4 |
| socle, prime radical | C22×C449 | C8 |
| cosocle | #16813311 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14368 |
928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#20297739, #43272893, #43272895, … |
| maximal normal subgroup of | C4×#20297739, #43272893, #43272895, … |
| maximal quotient of | C4×#20297739, C22⋊#20297739, C4⋊#20297739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 218);