Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of C5⋊(C11⋊D11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C5⋊(C11⋊D11) |
| unambiguous semidirect product | C11⋊D55 |
| Fitting, socle, derived, Hall | C5×C112 ⋊ C2 |
| Sylow | C112 ⋊ D5 |
| Sylow | C5 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 605 |
Polycyclic presentation:
2,5,11^2|b^a=b^4,c^a=c^10,d^a=d^10304 conjugacy classes — view the full character table.
| maximal subgroup of | #14559097, D5×C11⋊D11, D11×D55, … |
| maximal normal subgroup of | #14559097, D5×C11⋊D11, D11×D55, … |
| maximal quotient of | C11⋊Dic55, C2×C5⋊(C11⋊D11), C3×C5⋊(C11⋊D11), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 26);