Finite Group DatabasebetaFinite Group Databasebeta| order | 18492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C23×C67 ⋊ C22×C3 |
| Hall | D23×D67 ⋊ C3 |
| Hall | C23×C67⋊C3 ⋊ C22 |
| Hall | C67⋊C3 ⋊ C2×D23 |
| Sylow | C67 ⋊ C2×C3×D23 |
| Sylow | C23 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C67 | C22×C3 |
| LCS | G ▷ C23×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1541 |
221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18492, 14);