Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#20297748 |
| derived, Sylow | C449 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #16813320 |
| commutator, hypocenter | C449 | C2×C16 |
| Frattini | C2 | C2×#16813320 |
| Fitting, socle, prime radical | C22×C449 | C8 |
| cosocle | #16813318 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14368 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#20297748, #43273101, C22⋊#20297748, … |
| maximal normal subgroup of | C4×#20297748, #43273101, C22⋊#20297748, … |
| maximal quotient of | C4×#20297748, C22⋊#20297748, C4⋊#20297748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 240);