Finite Group Databasebeta

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C2×D19⋊C3×C121 #42119923

order27588
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D19⋊C3×C121
unambiguous semidirect productD19⋊(C2×C3×C121)
unambiguous semidirect product(C19⋊C3)⋊(C22×C121)
unambiguous semidirect product(C2×D19)⋊(C3×C121)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C121)
unambiguous semidirect product(C2×D19×C121)⋊C3

Splittings

FittingC2×C19×C121 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C3×C121
HallC2×D19×C121 ⋊ C3
HallC19⋊C3×C121 ⋊ C22
HallC19×C121 ⋊ C22×C3
HallC2×D19 ⋊ C3×C121
HallC19⋊C3 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D19⋊C3
commutator, hypocenterC19C22×C3×C121
FrattiniC11C2×C11×D19⋊C3
FittingC2×C19×C121C2×C3
socleC2×C11×C19C2×C3×C11
prime radicalC2×C11×D19⋊C3C11
cosocleC11×C19C22×C3×C11
LCSG ▷ C19
UCSC1 ◁ C2×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4598

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 15);