Finite Group DatabasebetaFinite Group Databasebeta| order | 15304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#21440083 |
| unambiguous semidirect product | D1913⋊C4 |
| Fitting, socle | C2×C1913 ⋊ C4 |
| derived, Sylow | C1913 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21440083 |
| commutator, hypocenter | C1913 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1913 | C4 |
| prime radical | C2×D1913 | C2 |
| cosocle | D1913 | C22 |
| LCS | G ▷ C1913 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3826 |
964 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#21440083, C22⋊#21440083, C4⋊#21440083, … |
| maximal normal subgroup of | C4×#21440083, C22⋊#21440083, C4⋊#21440083, … |
| maximal quotient of | C4×#21440083, C22⋊#21440083, C4⋊#21440083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15304, 14);