Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C137 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C13×C137 ⋊ C3 |
| derived, Hall | C22×C13 ⋊ C3×C137 |
| Hall | C13×C137 ⋊ A4 |
| Hall | C22×C137 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ A4×C137 |
| Sylow | C22 ⋊ C13⋊C3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | C22⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | C22×C13 | C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C137 | C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C137 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7124 |
2740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 44);