Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic111 |
| unambiguous semidirect product | C3⋊(C72×Dic37) |
| derived, Hall | C3×C37 ⋊ C4×C72 |
| Hall | C3×C72×C37 ⋊ C4 |
| Hall | C72×C37 ⋊ Dic3 |
| Hall | C3×C72 ⋊ Dic37 |
| Sylow | C37 ⋊ C72×Dic3 |
| Sylow | C3 ⋊ C72×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D111 |
| commutator, hypocenter | C3×C37 | C4×C72 |
| Frattini | C2 | C72×D111 |
| Fitting, socle, prime radical | C2×C3×C72×C37 | C2 |
| cosocle | C2×C3×C37 | C2×C72 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21756 |
5586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 146);