Finite Group DatabasebetaFinite Group Databasebeta| order | 18828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#17989920⋊C2 |
| unambiguous semidirect product | #17989920⋊C22 |
| unambiguous semidirect product | (C2×#17989920)⋊C2 |
| derived, Sylow | C523 ⋊ C22×C9 |
| Hall | #17989920 ⋊ C22 |
| Hall | C2×D523 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D523⋊C3 |
| commutator, hypocenter | C523 | C22×C9 |
| Frattini | C3 | C2×D523⋊C3 |
| Fitting, socle | C2×C3×C523 | C2×C3 |
| prime radical | C2×C3×D523 | C3 |
| cosocle | C3×C523 | C22×C3 |
| LCS | G ▷ C523 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9414 |
558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18828, 8);