Finite Group DatabasebetaFinite Group Databasebeta| order | 18124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D197 |
| unambiguous semidirect product | (D23×C197)⋊C2 |
| unambiguous semidirect product | (C23×D197)⋊C2 |
| unambiguous semidirect product | D4531⋊C2 |
| Fitting, socle, derived, Hall | C23×C197 ⋊ C22 |
| Sylow | C197 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D197 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C197 | C22 |
| LCS | G ▷ C23×C197 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4531 |
1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18124, 8);