Finite Group Databasebeta

← Prev (#37567638) Next (#37567640) →

C2×C3×D2035 #37567639

order24420
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2035
unambiguous semidirect product(C2×C5)⋊(C3×D407)
unambiguous semidirect product(C2×C11)⋊(C3×D185)

Splittings

Fitting, socleC2×C3×C5×C11×C37 ⋊ C2
derived, HallC5×C11×C37 ⋊ C22×C3
HallC3×C5×C11×C37 ⋊ C22
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×D55
HallC5×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C3×D55
HallC3×C11 ⋊ C2×D185
HallC3×C5 ⋊ C2×D407
SylowC11 ⋊ C2×C3×D185
SylowC5 ⋊ C2×C3×D407

Subgroups

subgroupG/H
center, hypercenterC2×C3D2035
commutator, cosocle, hypocenterC5×C11×C37C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C37C2
LCSG ▷ C5×C11×C37
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12210

Conjugacy classes & character table

6114 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 160);