Finite Group Databasebeta

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C4×C53×C31⋊C3 #34089301

order19716
automorphism?
homologyAbelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1

Aliases

direct productC4×C53×C31⋊C3
unambiguous semidirect product(C4×C31)⋊(C3×C53)
unambiguous semidirect product(C4×C31×C53)⋊C3

Splittings

Fitting, HallC4×C31×C53 ⋊ C3
derived, SylowC31 ⋊ C3×C4×C53
HallC31×C53 ⋊ C3×C4
HallC4×C31 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC4×C53C31⋊C3
commutator, hypocenterC31C3×C4×C53
FrattiniC2C2×C53×C31⋊C3
FittingC4×C31×C53C3
socleC2×C31×C53C2×C3
prime radicalC2×C53×C31⋊C3C2
cosocleC2×C31C2×C3×C53
LCSG ▷ C31
UCSC1 ◁ C4×C53

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6572

Conjugacy classes & character table

2756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19716, 2);