Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C13×C137 ⋊ C22×C3 |
| Hall | D13×D137 ⋊ C3 |
| Hall | C13⋊C3×C137 ⋊ C22 |
| Sylow | C137 ⋊ C2×D13⋊C3 |
| Hall | C13⋊C3 ⋊ C2×D137 |
| Sylow | C13 ⋊ C2×C3×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C137 | C22×C3 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1781 |
560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 19);