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C5×C13×D13⋊C3 #19099501

order5070
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C13)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C13)
unambiguous semidirect product(C5×D13)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C132 ⋊ C2×C3
derivedC13 ⋊ C2×C3×C5×C13
HallC5×C13×C13⋊C3 ⋊ C2
HallC5×C13×D13 ⋊ C3
HallC13×C13⋊C3 ⋊ C2×C5
HallC13×D13 ⋊ C3×C5
SylowC132 ⋊ C2×C3×C5

Subgroups

subgroupG/H
center, hypercenterC5×C13D13⋊C3
commutator, hypocenterC13C2×C3×C5×C13
FrattiniC1G
Fitting, socleC5×C132C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×D13⋊C3, C3×C5×C13×D13⋊C3, C5×C13×C3⋊(D13⋊C3), …
maximal normal subgroup ofC5×C13⋊C3×D13⋊C3, C3×C5×C13×D13⋊C3, C13×C25×D13⋊C3, …
maximal quotient ofC5×C13×D13⋊C9, C3×C5×C13×D13⋊C3, C5×C13×C3⋊(D13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5070, 14);