Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of #11925892 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C112 ⋊ C2×C5 |
| Hall | #10597243 ⋊ C2 |
| Hall | C11⋊D11 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 121 |
Polycyclic presentation:
2,5,11^2|c^a=c^10,d^a=d^10,c^b=c^4,d^b=d^422 conjugacy classes — view the full character table.
| maximal subgroup of | #11925892⋊C2, #92150⋊C5, C2×#11925892, … |
| maximal normal subgroup of | #11925892⋊C2, #92150⋊C5, C2×#11925892, … |
| maximal quotient of | #14559051, C2×#11925892, C3×#11925892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 9);