Finite Group Databasebeta

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C2×C19⋊C3×C43⋊C3 #28413685

order14706
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC2×C19⋊C3×C43⋊C3
unambiguous semidirect product(C2×C19×C43⋊C3)⋊C3
unambiguous semidirect product(C2×C43×C19⋊C3)⋊C3
unambiguous semidirect product(C2×#14578576)⋊C3
unambiguous semidirect product(C2×#14578575)⋊C3

Splittings

Fitting, socle, HallC2×C19×C43 ⋊ C32
derived, HallC19×C43 ⋊ C2×C32
HallC2×C43 ⋊ C3×C19⋊C3
SylowC43 ⋊ C2×C3×C19⋊C3
HallC2×C19 ⋊ C3×C43⋊C3
SylowC19 ⋊ C2×C3×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×C43⋊C3
commutator, cosocle, hypocenterC19×C43C2×C32
FrattiniC1G
Fitting, socleC2×C19×C43C32
LCSG ▷ C19×C43
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1634

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C19⋊C3)⋊((C43⋊C3)⋊C4), C43⋊C3×(C19⋊C3)⋊C4, C19⋊C3×(C43⋊C3)⋊C4, …
maximal normal subgroup of(C19⋊C3)⋊((C43⋊C3)⋊C4), C43⋊C3×(C19⋊C3)⋊C4, C19⋊C3×(C43⋊C3)⋊C4, …
maximal quotient ofC4×C19⋊C3×C43⋊C3, C22×C19⋊C3×C43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14706, 41);