Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×#20299799 |
| Fitting, socle, Hall | C3×C72×C37 ⋊ C4 |
| derived, Hall | C72×C37 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ #3866 |
| Hall | C3×C37 ⋊ #5997 |
| Sylow | C72 ⋊ C3×#3866 |
| Sylow | C37 ⋊ C3×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20299799 |
| commutator, hypocenter | C72×C37 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C37 | C4 |
| prime radical | C3×C7⋊D259 | C2 |
| cosocle | C7⋊D259 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
1371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 314);