Finite Group DatabasebetaFinite Group Databasebeta| order | 18972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C31 · Schur multiplier (H2) = C3 |
| direct product | C32×C31×Dic17 |
| derived, Sylow | C17 ⋊ C32×C4×C31 |
| Hall | C32×C17×C31 ⋊ C4 |
| Hall | C17×C31 ⋊ C32×C4 |
| Hall | C32×C17 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C31 | D17 |
| commutator, hypocenter | C17 | C32×C4×C31 |
| Frattini | C2 | C32×C31×D17 |
| Fitting, socle, prime radical | C2×C32×C17×C31 | C2 |
| cosocle | C2×C17 | C2×C32×C31 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C32×C31 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18972 |
5580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18972, 51);