Finite Group Databasebeta

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C5×C7×(C3⋊D3)⋊D13 #30655716

order16380
isoclinismisoclinic class of (C3⋊D3)⋊D13
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×(C3⋊D3)⋊D13
unambiguous semidirect product(C3⋊D3)⋊(C5×C7×D13)
unambiguous semidirect productD39⋊(C5×D3×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C22
derived, HallC32×C13 ⋊ C22×C5×C7
HallC32×C7×C13 ⋊ C22×C5
HallC32×C5×C13 ⋊ C22×C7
HallC5×C7×C13 ⋊ D32
HallC32×C5×C7 ⋊ C2×D13
HallC7×C13 ⋊ C5×D32
HallC5×C13 ⋊ D32×C7
HallC32×C7 ⋊ C2×C5×D13
HallC32×C5 ⋊ C2×C7×D13
SylowC13 ⋊ C5×D32×C7
SylowC32 ⋊ C2×C5×C7×D13

Subgroups

subgroupG/H
center, hypercenterC5×C7(C3⋊D3)⋊D13
commutator, cosocle, hypocenterC32×C13C22×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C32×C13
UCSC1 ◁ C5×C7

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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

1575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 766);