Finite Group DatabasebetaFinite Group Databasebeta| order | 18492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊((C67⋊C3)⋊C4) |
| unambiguous semidirect product | (C67⋊C3)⋊Dic23 |
| unambiguous semidirect product | Dic1541⋊C3 |
| derived, Hall | C23×C67 ⋊ C3×C4 |
| Hall | Dic1541 ⋊ C3 |
| Hall | C23×C67⋊C3 ⋊ C4 |
| Hall | C67⋊C3 ⋊ Dic23 |
| Sylow | C67 ⋊ C3×Dic23 |
| Sylow | C23 ⋊ (C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊(D67⋊C3) |
| commutator, hypocenter | C23×C67 | C3×C4 |
| Fitting, socle, cosocle | C2×C23×C67 | C2×C3 |
| prime radical | C2×C23×C67⋊C3 | C2 |
| LCS | G ▷ C23×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6164 |
Polycyclic presentation:
2,3,23,67,2|a^2=e,c^a=c^22,d^a=d^66,d^b=d^37584 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18492, 12);