Finite Group Databasebeta

← Prev (#35234385) Next (#35234387) →

C3×C31×(C19⋊C3)⋊C4 #35234386

order21204
automorphism?
homologyAbelianization (H1) = C32×C4×C31 · Schur multiplier (H2) = C3

Aliases

direct productC3×C31×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C3×C4×C31)
unambiguous semidirect productDic19⋊(C32×C31)
unambiguous semidirect product(C3×Dic19)⋊(C3×C31)

Splittings

derived, SylowC19 ⋊ C32×C4×C31
HallC3×C31×C19⋊C3 ⋊ C4
HallC31×Dic19 ⋊ C32
HallC19×C31 ⋊ C32×C4
HallC3×C19⋊C3 ⋊ C4×C31
HallDic19 ⋊ C32×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D19⋊C3
commutator, hypocenterC19C32×C4×C31
FrattiniC2C3×C31×D19⋊C3
Fitting, socleC2×C3×C19×C31C2×C3
prime radicalC2×C3×C31×C19⋊C3C2
cosocleC2×C19C2×C32×C31
LCSG ▷ C19
UCSC1 ◁ C2×C3×C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7068

Conjugacy classes & character table

1674 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 83);