Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#15692423 |
| derived, Sylow | C361 ⋊ C5×C9 |
| Hall | C5×C361 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C361⋊C3 |
| commutator, hypocenter | C361 | C5×C9 |
| Frattini | C3×C19 | C5×C19⋊C3 |
| Fitting | C3×C5×C361 | C3 |
| socle, prime radical | C3×C5×C19 | C19⋊C3 |
| cosocle | C3×C361 | C3×C5 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C3×C5 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
1845 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#15692423⋊C2, D5×#15692423, C5⋊(#15692423⋊C2), … |
| maximal normal subgroup of | C5×#15692423⋊C2, D5×#15692423, C5⋊(#15692423⋊C2), … |
| maximal quotient of | C2×C5×#15692423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 2);