Finite Group Databasebeta

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D7×C3⋊D165 #28357705

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

Aliases

direct productD7×C3⋊D165
unambiguous semidirect product(C3×D7)⋊D165
unambiguous semidirect product(C5×D7)⋊(C3⋊D33)
unambiguous semidirect product(C11×D7)⋊(C3⋊D15)

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C11C22
LCSG ▷ C32×C5×C7×C11
UCSC1

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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

1245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 372);