Finite Group Databasebeta

← Prev (#30655598) Next (#30655600) →

C2×C7×C3⋊(C5⋊(D13⋊C3)) #30655599

order16380
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C3⋊(C5⋊(D13⋊C3))
unambiguous semidirect product(C2×C3)⋊(C7×C5⋊(D13⋊C3))
unambiguous semidirect product(C2×C5)⋊(C7×C3⋊(D13⋊C3))
unambiguous semidirect product(C2×C13⋊C3)⋊(C7×D15)
unambiguous semidirect product(C2×D195)⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C22×C3×C7
HallC3×C5×C7×C13⋊C3 ⋊ C22
HallC3×C7×C13⋊C3 ⋊ C2×D5
HallC3×C5×C13⋊C3 ⋊ C22×C7
HallC5×C7×C13 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C2×C7×D5
HallC7×C13 ⋊ C2×C3×D15
HallC5×C13 ⋊ C2×C3×D3×C7
HallC5×C7 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C2×C3×C7×D15
SylowC5 ⋊ C2×C7×C3⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊(D13⋊C3))
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C7

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 649);