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D13⋊C3×C131 #23779343

order10218
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C131 · Schur multiplier (H2) = C1

Aliases

direct productD13⋊C3×C131
unambiguous semidirect productD13⋊(C3×C131)
unambiguous semidirect product(C13⋊C3)⋊(C2×C131)
unambiguous semidirect product(D13×C131)⋊C3

Splittings

Fitting, socle, HallC13×C131 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C131
HallC13⋊C3×C131 ⋊ C2
HallD13×C131 ⋊ C3
HallC13⋊C3 ⋊ C2×C131
HallD13 ⋊ C3×C131

Subgroups

subgroupG/H
center, hypercenterC131D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C131
FrattiniC1G
Fitting, socleC13×C131C2×C3
LCSG ▷ C13
UCSC1 ◁ C131

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC131×AGL(1,𝔽13), C131⋊AGL(1,𝔽13), D13⋊C3×D131, …
maximal normal subgroup ofC131×AGL(1,𝔽13), C131⋊AGL(1,𝔽13), D13⋊C3×D131, …
maximal quotient ofC131×Dic13⋊C3, C2×D13⋊C3×C131, C131×D13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10218, 15);