Finite Group DatabasebetaFinite Group Databasebeta| order | 29820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C71 | C22×C5×C7 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 213 |
213 conjugacy classes — view the full character table.
| holomorph of | C3×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29820, 50);