Finite Group Databasebeta

C2×C19×D31⋊C9 #35234333

order21204
automorphism?
homologyAbelianization (H1) = C22×C9×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×D31⋊C9
unambiguous semidirect productD31⋊(C2×C9×C19)
unambiguous semidirect product(C2×D31)⋊(C9×C19)
unambiguous semidirect product(C31⋊C9)⋊(C22×C19)
unambiguous semidirect product(C2×C31⋊C9)⋊(C2×C19)

Splittings

derived, SylowC31 ⋊ C22×C9×C19
HallC19×C31⋊C9 ⋊ C22
HallC2×C19×D31 ⋊ C9
HallC19×C31 ⋊ C22×C9
HallC31⋊C9 ⋊ C22×C19
HallC2×D31 ⋊ C9×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D31⋊C3
commutator, hypocenterC31C22×C9×C19
FrattiniC3C2×C19×D31⋊C3
Fitting, socleC2×C3×C19×C31C2×C3
prime radicalC2×C3×C19×D31C3
cosocleC3×C31C22×C3×C19
LCSG ▷ C31
UCSC1 ◁ C2×C3×C19

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10602

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, 30);