Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of #10597243 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×#10597243 |
| Fitting, socle, Hall | C2×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10597243 |
| commutator, cosocle, hypocenter | C112 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 242 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #14559051, #14559054, C4×#10597243, … |
| maximal normal subgroup of | #14559051, #14559054, C4×#10597243, … |
| maximal quotient of | C4×#10597243, C22×#10597243, D3×#10597243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 19);