Finite Group Databasebeta

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C4×C19⋊C3×C31⋊C3 #35234384

order21204
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×C19⋊C3×C31⋊C3
unambiguous semidirect product(C4×C19×C31⋊C3)⋊C3
unambiguous semidirect product(C4×C31×C19⋊C3)⋊C3
unambiguous semidirect product(C4×#13183715)⋊C3
unambiguous semidirect product(C4×#13183714)⋊C3

Splittings

Fitting, HallC4×C19×C31 ⋊ C32
derived, HallC19×C31 ⋊ C32×C4
HallC4×C31 ⋊ C3×C19⋊C3
HallC4×C19 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×C4×C19⋊C3
SylowC19 ⋊ C3×C4×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C19⋊C3×C31⋊C3
commutator, hypocenterC19×C31C32×C4
FrattiniC2C2×C19⋊C3×C31⋊C3
FittingC4×C19×C31C32
socle, cosocleC2×C19×C31C2×C32
prime radicalC2×C19⋊C3×C31⋊C3C2
LCSG ▷ C19×C31
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2356

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 81);