Finite Group Databasebeta

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C2×C3×C5×C13×D13⋊C3 #44478147

order30420
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×C13×D13⋊C3
unambiguous semidirect productD13⋊(C2×C32×C5×C13)
unambiguous semidirect product(C13⋊C3)⋊(C22×C3×C5×C13)
unambiguous semidirect product(C2×D13)⋊(C32×C5×C13)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C3×C5×C13)
unambiguous semidirect product(C2×C3×D13)⋊(C3×C5×C13)
unambiguous semidirect product(C2×C5×D13)⋊(C32×C13)
unambiguous semidirect product(C2×C3×C5×D13)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C5×C132 ⋊ C2×C3
derivedC13 ⋊ C22×C32×C5×C13
HallC3×C5×C13×C13⋊C3 ⋊ C22
HallC2×C5×C13×D13 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ C22×C5
HallC5×C132 ⋊ C22×C32
HallC2×C13×D13 ⋊ C32×C5
SylowC132 ⋊ C22×C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13D13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C132C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C13

256 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 136 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

3120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 736);