Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C5×C192 ⋊ C32 |
| derived, Sylow | C192 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C19⋊C32 |
| commutator, cosocle, hypocenter | C192 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C32 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#14524212⋊C3, C5×C19⋊C3×D19⋊C3, C5×(C19⋊C3)⋊(D19⋊C3), … |
| maximal normal subgroup of | C5×#14524212⋊C3, C5×C19⋊C3×D19⋊C3, C5×(C19⋊C3)⋊(D19⋊C3), … |
| maximal quotient of | C2×C5×C19⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 22);