Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#24925958 |
| Fitting, socle | C2×C72×C37 ⋊ C2×C3 |
| derived, Hall | C72×C37 ⋊ C22×C3 |
| Hall | C2×C7×D259 ⋊ C3 |
| Hall | #19129589 ⋊ C22 |
| Sylow | C72 ⋊ C2×D37⋊C3 |
| Sylow | C37 ⋊ C2×#64423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #24925958 |
| commutator, cosocle, hypocenter | C72×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1036 |
622 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 294);