Finite Group DatabasebetaFinite Group Databasebeta| order | 19026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C151 · Schur multiplier (H2) = C1 |
| direct product | C2×C7⋊C9×C151 |
| unambiguous semidirect product | (C2×C7)⋊(C9×C151) |
| derived, Sylow | C7 ⋊ C2×C9×C151 |
| Hall | C2×C7×C151 ⋊ C9 |
| Hall | C7×C151 ⋊ C2×C9 |
| Hall | C2×C7 ⋊ C9×C151 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19026 |
4530 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7⋊C9×C151, C7⋊C9×Dic151, C151×Dic7⋊C9, … |
| maximal normal subgroup of | C4×C7⋊C9×C151, C7⋊C9×Dic151, C151×Dic7⋊C9, … |
| maximal quotient of | C4×C7⋊C9×C151, C22×C7⋊C9×C151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19026, 3);