Finite Group Databasebeta

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C2×C3⋊(C5⋊((C13⋊C3)⋊D7)) #30655613

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

Aliases

direct productC2×C3⋊(C5⋊((C13⋊C3)⋊D7))
unambiguous semidirect product(C2×C3)⋊(C5⋊((C13⋊C3)⋊D7))
unambiguous semidirect product(C2×C5)⋊(C3⋊((C13⋊C3)⋊D7))
unambiguous semidirect product(C2×C13⋊C3)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2×C3
derivedC3×C5×C7×C13 ⋊ C22×C3
HallC3×C5×C7×C13⋊C3 ⋊ C22
HallC3×C7×C13⋊C3 ⋊ C2×D5
HallC3×C5×C13⋊C3 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C2×D35
HallC7×C13 ⋊ C2×C3×D15
HallC5×C13 ⋊ C2×C3×D21
HallC5×C7 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C2×C3×D105
SylowC7 ⋊ C2×C3⋊(C5⋊(D13⋊C3))
SylowC5 ⋊ C2×C3⋊((C13⋊C3)⋊D7)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊((C13⋊C3)⋊D7))
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2×C3
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C2

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 2730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 663);