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C2×C13×D43⋊C3 #20269458

order6708
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D43⋊C3
unambiguous semidirect productD43⋊(C2×C3×C13)
unambiguous semidirect product(C43⋊C3)⋊(C22×C13)
unambiguous semidirect product(C2×D43)⋊(C3×C13)
unambiguous semidirect product(C2×C43⋊C3)⋊(C2×C13)

Splittings

Fitting, socleC2×C13×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C22×C3×C13
HallC2×C13×D43 ⋊ C3
HallC13×C43⋊C3 ⋊ C22
HallC13×C43 ⋊ C22×C3
HallC2×D43 ⋊ C3×C13
HallC43⋊C3 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D43⋊C3
commutator, hypocenterC43C22×C3×C13
FrattiniC1G
Fitting, socleC2×C13×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C2×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13⋊C3×D43⋊C3, D3×C13×D43⋊C3, C2×C3×C13×D43⋊C3, …
maximal normal subgroup ofC2×C13⋊C3×D43⋊C3, C2×C3×C13×D43⋊C3, C2×C5×C13×D43⋊C3
maximal quotient ofC2×C13×D43⋊C9, D3×C13×D43⋊C3, C2×C3×C13×D43⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6708, 38);