Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of #11925890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C112 ⋊ D5 |
| derived, Hall | #10597245 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #10597245 | C2 |
| Fitting, socle | C112 | D5 |
| LCS | G ▷ #10597245 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 22 |
Polycyclic presentation:
2,5,11^2|b^a=b^4,c^a=d,d^a=c,c^b=c^4,d^b=d^331 conjugacy classes — view the full character table.
| maximal subgroup of | #11925890⋊C2, C2×#11925890, C3×#11925890, … |
| maximal normal subgroup of | #11925890⋊C2, C2×#11925890, C3×#11925890, … |
| maximal quotient of | #14559049, C2×#11925890, C3×#11925890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 7);