Finite Group Databasebeta

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C2×C3×C13×D19⋊C3 #22580318

order8892
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C13×D19⋊C3
unambiguous semidirect productD19⋊(C2×C32×C13)
unambiguous semidirect product(C19⋊C3)⋊(C22×C3×C13)
unambiguous semidirect product(C2×D19)⋊(C32×C13)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C3×C13)
unambiguous semidirect product(C2×C3×D19)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C13×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C32×C13
HallC3×C13×C19⋊C3 ⋊ C22
HallC2×C13×D19 ⋊ C32
HallC13×C19 ⋊ C22×C32
HallC3×C19⋊C3 ⋊ C22×C13
HallC2×D19 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D19⋊C3
commutator, hypocenterC19C22×C32×C13
FrattiniC1G
Fitting, socleC2×C3×C13×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

702 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 221);