Finite Group Databasebeta

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C3×D3×C7×D5×C11 #28357676

order13860
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×D3×C7×D5×C11
unambiguous semidirect product(C5×D3)⋊(C2×C3×C7×C11)
unambiguous semidirect product(C3×D5)⋊(C2×C3×C7×C11)
unambiguous semidirect productD15⋊(C2×C3×C7×C11)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derivedC3×C5 ⋊ C22×C3×C7×C11
HallC32×C7×C11 ⋊ C2×D5
HallC32×C5×C11 ⋊ C22×C7
HallC5×C7×C11 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C22×C11
HallC32×C11 ⋊ C2×C7×D5
HallC32×C7 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C3×D3×C7
HallC32×C5 ⋊ C22×C7×C11
HallC5×C7 ⋊ C2×C3×D3×C11
SylowC32 ⋊ C2×C7×D5×C11
SylowC5 ⋊ C2×C3×D3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D3×D5
commutator, cosocle, hypocenterC3×C5C22×C3×C7×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C3×C5
UCSC1 ◁ C3×C7×C11

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 2310

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 343);