Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C137 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic13×C137 |
| derived, Sylow | C13 ⋊ C3×C4×C137 |
| Hall | C3×C13×C137 ⋊ C4 |
| Hall | C13×C137 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ C4×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C137 | D13 |
| commutator, hypocenter | C13 | C3×C4×C137 |
| Frattini | C2 | C3×D13×C137 |
| Fitting, socle, prime radical | C2×C3×C13×C137 | C2 |
| cosocle | C2×C13 | C2×C3×C137 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3×C137 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21372 |
6576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 4);