Finite Group Databasebeta

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C2×C5×C13×D19⋊C3 #28414840

order14820
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D19⋊C3
unambiguous semidirect productD19⋊(C2×C3×C5×C13)
unambiguous semidirect product(C19⋊C3)⋊(C22×C5×C13)
unambiguous semidirect product(C2×D19)⋊(C3×C5×C13)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C5×C13)
unambiguous semidirect product(C2×C5×D19)⋊(C3×C13)

Splittings

Fitting, socleC2×C5×C13×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C3×C5×C13
HallC2×C5×C13×D19 ⋊ C3
HallC5×C13×C19⋊C3 ⋊ C22
HallC5×C13×C19 ⋊ C22×C3
HallC2×C13×D19 ⋊ C3×C5
HallC13×C19⋊C3 ⋊ C22×C5
HallC2×C5×D19 ⋊ C3×C13
HallC5×C19⋊C3 ⋊ C22×C13
HallC13×C19 ⋊ C22×C3×C5
HallC5×C19 ⋊ C22×C3×C13
HallC2×D19 ⋊ C3×C5×C13
HallC19⋊C3 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D19⋊C3
commutator, cosocle, hypocenterC19C22×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C5×C13×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2470

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 126);