Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#3866⋊C3 |
| unambiguous semidirect product | #3866⋊(C3×C72) |
| Fitting, socle, Hall | C72×C37 ⋊ C3×C4 |
| derived, Sylow | C37 ⋊ C3×C4×C72 |
| Hall | C72×#3866 ⋊ C3 |
| Hall | C72×C37⋊C3 ⋊ C4 |
| Hall | #3866 ⋊ C3×C72 |
| Hall | C37⋊C3 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #3866⋊C3 |
| commutator, hypocenter | C37 | C3×C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C3×C4 |
| prime radical | C72×D37⋊C3 | C2 |
| cosocle | D37 | C2×C3×C72 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 174);