Finite Group Databasebeta

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C3×D7×D165 #28357673

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

Aliases

direct productC3×D7×D165

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derivedC3×C5×C7×C11 ⋊ C22×C3
HallC32×C7×C11 ⋊ C2×D5
HallC32×C5×C11 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D11
HallC32×C11 ⋊ D5×D7
HallC7×C11 ⋊ C2×C3×D15
HallC32×C7 ⋊ C2×D55
HallC5×C11 ⋊ C3×D3×D7
HallC32×C5 ⋊ D7×D11
HallC5×C7 ⋊ C2×C3×D33
SylowC11 ⋊ C3×D7×D15
SylowC32 ⋊ D7×D55
SylowC7 ⋊ C2×C3×D165
SylowC5 ⋊ C3×D7×D33

Subgroups

subgroupG/H
center, hypercenterC3D7×D165
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 340);