Finite Group DatabasebetaFinite Group Databasebeta| order | 22204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C61 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic7×C61 |
| unambiguous semidirect product | C7⋊(C4×C13×C61) |
| derived, Sylow | C7 ⋊ C4×C13×C61 |
| Hall | C7×C13×C61 ⋊ C4 |
| Hall | C7×C61 ⋊ C4×C13 |
| Hall | C7×C13 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13×C61 | D7 |
| commutator, hypocenter | C7 | C4×C13×C61 |
| Frattini | C2 | C13×D7×C61 |
| Fitting, socle, prime radical | C2×C7×C13×C61 | C2 |
| cosocle | C2×C7 | C2×C13×C61 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C13×C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22204 |
7930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22204, 5);