Finite Group DatabasebetaFinite Group Databasebeta| order | 18699 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C271⋊C3 |
| unambiguous semidirect product | C271⋊(C3×C23) |
| unambiguous semidirect product | (C23×C271)⋊C3 |
| Fitting, socle, Hall | C23×C271 ⋊ C3 |
| derived, Sylow | C271 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C271⋊C3 |
| commutator, cosocle, hypocenter | C271 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C271 | C3 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6233 |
2139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×C271⋊C3, C23×D271⋊C3, D23×C271⋊C3, … |
| maximal normal subgroup of | C2×C23×C271⋊C3, C23×D271⋊C3, D23×C271⋊C3, … |
| maximal quotient of | C2×C23×C271⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18699, 1);