Finite Group DatabasebetaFinite Group Databasebeta| order | 24198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C109 · Schur multiplier (H2) = C1 |
| direct product | C2×C109×C37⋊C3 |
| unambiguous semidirect product | (C2×C37)⋊(C3×C109) |
| Fitting, socle, Hall | C2×C37×C109 ⋊ C3 |
| derived, Sylow | C37 ⋊ C2×C3×C109 |
| Hall | C37×C109 ⋊ C2×C3 |
| Hall | C2×C37 ⋊ C3×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C109 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C109 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C109 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C109 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8066 |
3270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24198, 3);