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C32×C7×D5×D11 #28357654

order13860
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×C7×D5×D11
unambiguous semidirect product(D5×C11)⋊(C2×C32×C7)
unambiguous semidirect product(C5×D11)⋊(C2×C32×C7)
unambiguous semidirect productD55⋊(C2×C32×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derived, HallC5×C11 ⋊ C22×C32×C7
HallC32×C7×C11 ⋊ C2×D5
HallC32×C5×C11 ⋊ C22×C7
HallC5×C7×C11 ⋊ C22×C32
HallC32×C5×C7 ⋊ C2×D11
HallC32×C11 ⋊ C2×C7×D5
HallC7×C11 ⋊ C2×C32×D5
HallC32×C5 ⋊ C2×C7×D11
HallC5×C7 ⋊ C2×C32×D11
SylowC11 ⋊ C2×C32×C7×D5
SylowC5 ⋊ C2×C32×C7×D11

Subgroups

subgroupG/H
center, hypercenterC32×C7D5×D11
commutator, cosocle, hypocenterC5×C11C22×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C5×C11
UCSC1 ◁ C32×C7

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 3465

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 321);