Finite Group DatabasebetaFinite Group Databasebeta| order | 18492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2 |
| direct product | C22×C23×C67⋊C3 |
| Fitting, socle, Hall | C22×C23×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C22×C3×C23 |
| Hall | C23×C67 ⋊ C22×C3 |
| Hall | C22×C67 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C23 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C22×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C23×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C22×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6164 |
2300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18492, 27);