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C3×C7×D5×D13⋊C3 #30655355

order16380
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×D5×D13⋊C3
unambiguous semidirect productD13⋊(C32×C7×D5)
unambiguous semidirect product(D5×D13)⋊(C32×C7)
unambiguous semidirect product(C5×D13⋊C3)⋊(C2×C3×C7)
unambiguous semidirect product(D5×C13⋊C3)⋊(C2×C3×C7)
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C2×C3×C7)
unambiguous semidirect product(C3×D5×D13)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C22×C3
derived, HallC5×C13 ⋊ C22×C32×C7
HallC3×C5×C7×C13⋊C3 ⋊ C22
HallC7×D5×D13 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ C2×D5
HallC3×C5×C13⋊C3 ⋊ C22×C7
HallC5×C7×C13 ⋊ C22×C32
HallD5×D13 ⋊ C32×C7
HallC3×C13⋊C3 ⋊ C2×C7×D5
HallC7×C13 ⋊ C2×C32×D5
HallC5×C7 ⋊ C2×C3×D13⋊C3
SylowC13 ⋊ C2×C32×C7×D5
SylowC5 ⋊ C2×C3×C7×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C32×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C7

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 405);