Finite Group Databasebeta

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C5×A4×C13×C13⋊C3 #44478139

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

Aliases

direct productC5×A4×C13×C13⋊C3
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C5×C13)
unambiguous semidirect product(A4×C13)⋊(C3×C5×C13)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C5×C13)
unambiguous semidirect product(C22×C5×C13⋊C3)⋊(C3×C13)
unambiguous semidirect product(C5×A4×C13)⋊(C3×C13)
unambiguous semidirect product(C5×C22⋊(C13⋊C3))⋊(C3×C13)

Splittings

Fitting, socle, HallC22×C5×C132 ⋊ C32
derivedC22×C13 ⋊ C32×C5×C13
HallC5×C132 ⋊ C3×A4
HallC22×C132 ⋊ C32×C5
SylowC132 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C13×C13⋊C3
SylowC22 ⋊ C3×C5×C13×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C13A4×C13⋊C3
commutator, cosocle, hypocenterC22×C13C32×C5×C13
FrattiniC1G
Fitting, socleC22×C5×C132C32
LCSG ▷ C22×C13
UCSC1 ◁ C5×C13

152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 780

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 728);