Finite Group Databasebeta

← Prev (#30655564) Next (#30655566) →

C2×C3×C5×(C13⋊C3)⋊D7 #30655565

order16380
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×(C13⋊C3)⋊D7
unambiguous semidirect product(C2×C13⋊C3)⋊(C3×C5×D7)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C32×C5
HallC3×C5×C7×C13⋊C3 ⋊ C22
HallC2×C5×D91 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ C22×C5
HallC3×C5×C13⋊C3 ⋊ C2×D7
HallC5×C7×C13 ⋊ C22×C32
HallC2×D91 ⋊ C32×C5
HallC3×C13⋊C3 ⋊ C2×C5×D7
HallC5×C13 ⋊ C2×C32×D7
HallC5×C7 ⋊ C2×C3×D13⋊C3
SylowC13 ⋊ C2×C32×C5×D7
SylowC7 ⋊ C2×C3×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 615);