Finite Group Databasebeta

← Prev (#26042598) Next (#26042600) →

C3×(C19⋊C3)⋊Dic17 #26042599

order11628
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C19⋊C3)⋊Dic17
unambiguous semidirect product(C19⋊C3)⋊(C3×Dic17)
unambiguous semidirect productDic323⋊C32
unambiguous semidirect product(C3×Dic323)⋊C3

Splittings

derived, HallC17×C19 ⋊ C32×C4
HallC3×C17×C19⋊C3 ⋊ C4
HallDic323 ⋊ C32
HallC3×C19⋊C3 ⋊ Dic17
SylowC19 ⋊ C32×Dic17
SylowC17 ⋊ C3×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C17⋊(D19⋊C3)
commutator, hypocenterC17×C19C32×C4
FrattiniC2C3×C17⋊(D19⋊C3)
Fitting, socleC2×C3×C17×C19C2×C3
prime radicalC2×C3×C17×C19⋊C3C2
cosocleC2×C17×C19C2×C32
LCSG ▷ C17×C19
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

486 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 47);