Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#19129589 |
| Fitting, Hall | C4×C72×C37 ⋊ C3 |
| derived, Hall | C72×C37 ⋊ C3×C4 |
| Hall | C4×C72 ⋊ C37⋊C3 |
| Hall | C4×C37 ⋊ #3861 |
| Sylow | C72 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ C4×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19129589 |
| commutator, hypocenter | C72×C37 | C3×C4 |
| Frattini | C2 | C2×#19129589 |
| Fitting | C4×C72×C37 | C3 |
| socle, cosocle | C2×C72×C37 | C2×C3 |
| prime radical | C2×#19129589 | C2 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C4 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7252 |
2428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 138);