Finite Group Databasebeta

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C4×C5×C13⋊C32 #44477805

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC4×C5×C13⋊C32
unambiguous semidirect product(C4×C13×C13⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×#92788)⋊(C3×C5)
unambiguous semidirect product(C4×#92789)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C13×C13⋊C3)⋊C3
unambiguous semidirect product(C4×C5×#92788)⋊C3
unambiguous semidirect product(C4×C5×#92789)⋊C3

Splittings

Fitting, HallC4×C5×C132 ⋊ C32
derived, SylowC132 ⋊ C32×C4×C5
HallC5×C132 ⋊ C32×C4
HallC4×C132 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C13⋊C32
commutator, hypocenterC132C32×C4×C5
FrattiniC2C2×C5×C13⋊C32
FittingC4×C5×C132C32
socleC2×C5×C132C2×C32
prime radicalC2×C5×C13⋊C32C2
cosocleC2×C132C2×C32×C5
LCSG ▷ C132
UCSC1 ◁ C4×C5

192 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 66 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 394);