Finite Group Databasebeta

← Prev (#35234384) Next (#35234386) →

C3×C19×(C31⋊C3)⋊C4 #35234385

order21204
automorphism?
homologyAbelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3

Aliases

direct productC3×C19×(C31⋊C3)⋊C4
unambiguous semidirect product(C31⋊C3)⋊(C3×C4×C19)
unambiguous semidirect productDic31⋊(C32×C19)
unambiguous semidirect product(C3×Dic31)⋊(C3×C19)

Splittings

derived, SylowC31 ⋊ C32×C4×C19
HallC3×C19×C31⋊C3 ⋊ C4
HallC19×Dic31 ⋊ C32
HallC19×C31 ⋊ C32×C4
HallC3×C31⋊C3 ⋊ C4×C19
HallDic31 ⋊ C32×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D31⋊C3
commutator, hypocenterC31C32×C4×C19
FrattiniC2C3×C19×D31⋊C3
Fitting, socleC2×C3×C19×C31C2×C3
prime radicalC2×C3×C19×C31⋊C3C2
cosocleC2×C31C2×C32×C19
LCSG ▷ C31
UCSC1 ◁ C2×C3×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7068

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 82);