Finite Group DatabasebetaFinite Group Databasebeta| order | 1962 |
| isoclinism | isoclinic class of C109⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#11758279 |
| derived, Sylow | C109 ⋊ C2×C9 |
| Hall | C2×C109 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C109⋊C3 |
| commutator, hypocenter | C109 | C2×C9 |
| Frattini | C3 | C2×C109⋊C3 |
| Fitting, socle, prime radical | C2×C3×C109 | C3 |
| cosocle | C3×C109 | C2×C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 120 |
| transitive degree | μt(G) = 1962 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | #16840975, C4×#11758279, C2×#11758279⋊C2, … |
| maximal normal subgroup of | #16840975, C4×#11758279, C2×#11758279⋊C2, … |
| maximal quotient of | C4×#11758279, C22×#11758279, C2×C7×#11758279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1962, 2);