Finite Group DatabasebetaFinite Group Databasebeta| order | 21324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#20297040 |
| Fitting, socle, Hall | C3×C1777 ⋊ C4 |
| derived, Sylow | C1777 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20297040 |
| commutator, hypocenter | C1777 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1777 | C4 |
| prime radical | C3×D1777 | C2 |
| cosocle | D1777 | C2×C3 |
| LCS | G ▷ C1777 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5331 |
1344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21324, 10);