Finite Group Databasebeta

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C2×C3×C13×C5⋊(D13⋊C3) #44478156

order30420
automorphism?
homologyAbelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C13×C5⋊(D13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C3×C13×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C3×D5×C13)
unambiguous semidirect product(C2×D65)⋊(C32×C13)
unambiguous semidirect product(C2×C3×D65)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C5×C132 ⋊ C2×C3
derivedC5×C13 ⋊ C22×C32×C13
HallC3×C5×C13×C13⋊C3 ⋊ C22
HallC2×C13×D65 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ C2×D5
HallC5×C132 ⋊ C22×C32
SylowC132 ⋊ C2×C32×D5
SylowC5 ⋊ C2×C3×C13×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C22×C32×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C132C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C13

256 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 2340

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 745);