Finite Group DatabasebetaFinite Group Databasebeta| order | 28158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#28381091 |
| Fitting, Hall | C2×C13×C361 ⋊ C3 |
| derived, Hall | C13×C361 ⋊ C2×C3 |
| Hall | C2×C361 ⋊ C13⋊C3 |
| Sylow | C361 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C361⋊C3 |
| Sylow | C13 ⋊ C2×C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #28381091 |
| commutator, cosocle, hypocenter | C13×C361 | C2×C3 |
| Frattini | C19 | C2×#10625202 |
| Fitting | C2×C13×C361 | C3 |
| socle | C2×C13×C19 | C19⋊C3 |
| LCS | G ▷ C13×C361 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9386 |
3134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28158, 16);