Finite Group Databasebeta

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C19×C3⋊((C31⋊C3)⋊C4) #35234397

order21204
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C19×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(Dic3×C19)
unambiguous semidirect productDic93⋊(C3×C19)

Splittings

derivedC3×C31 ⋊ C3×C4×C19
HallC3×C19×C31⋊C3 ⋊ C4
HallC19×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C4×C19
SylowC31 ⋊ C3×Dic3×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19C3⋊(D31⋊C3)
commutator, hypocenterC3×C31C3×C4×C19
FrattiniC2C19×C3⋊(D31⋊C3)
Fitting, socleC2×C3×C19×C31C2×C3
prime radicalC2×C3×C19×C31⋊C3C2
cosocleC2×C3×C31C2×C3×C19
LCSG ▷ C3×C31
UCSC1 ◁ C2×C19

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7068

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 94);