Finite Group DatabasebetaFinite Group Databasebeta| order | 18492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊D67 |
| unambiguous semidirect product | D201⋊D23 |
| unambiguous semidirect product | D1541⋊D3 |
| Fitting, socle, derived, Hall | C3×C23×C67 ⋊ C22 |
| Hall | C23×C67 ⋊ C2×D3 |
| Hall | C3×C67 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D67 |
| Sylow | C67 ⋊ D3×D23 |
| Sylow | C23 ⋊ D3×D67 |
| Sylow | C3 ⋊ D23×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C67 | C22 |
| LCS | G ▷ C3×C23×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4623 |
Polycyclic presentation:
2^2,3,23,67|d^a=d^22,e^a=e^66,c^b=c^2,d^b=d^221227 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18492, 24);