Finite Group DatabasebetaFinite Group Databasebeta| order | 18174 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C233 · Schur multiplier (H2) = C1 |
| direct product | C2×C13⋊C3×C233 |
| unambiguous semidirect product | (C2×C13)⋊(C3×C233) |
| unambiguous semidirect product | (C2×C13×C233)⋊C3 |
| Fitting, socle, Hall | C2×C13×C233 ⋊ C3 |
| derived, Sylow | C13 ⋊ C2×C3×C233 |
| Hall | C13×C233 ⋊ C2×C3 |
| Hall | C2×C13 ⋊ C3×C233 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C233 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C233 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C233 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C233 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6058 |
3262 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C13⋊C3×C233, C13⋊C3×Dic233, Dic13⋊C3×C233, … |
| maximal normal subgroup of | C4×C13⋊C3×C233, C13⋊C3×Dic233, Dic13⋊C3×C233, … |
| maximal quotient of | C4×C13⋊C3×C233, C22×C13⋊C3×C233 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18174, 2);