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C25×C3⋊(D13⋊C3) #19154302

order5850
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×C3⋊(D13⋊C3)
unambiguous semidirect productC3⋊(C25×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D3×C25)
unambiguous semidirect productD39⋊(C3×C25)
unambiguous semidirect product(C25×D39)⋊C3

Splittings

FittingC3×C13×C25 ⋊ C2×C3
derivedC3×C13 ⋊ C2×C3×C25
HallC3×C25×C13⋊C3 ⋊ C2
HallC13×C25 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C2×C25
SylowC13 ⋊ C3×D3×C25

Subgroups

subgroupG/H
center, hypercenterC25C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C2×C3×C25
FrattiniC5C5×C3⋊(D13⋊C3)
FittingC3×C13×C25C2×C3
socleC3×C5×C13C2×C3×C5
LCSG ▷ C3×C13
UCSC1 ◁ C25

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C25×D13⋊C3, D25×C3⋊(D13⋊C3), D75⋊(D13⋊C3), …
maximal normal subgroup ofD3×C25×D13⋊C3, D25×C3⋊(D13⋊C3), D75⋊(D13⋊C3), …
maximal quotient ofC25×C3⋊(Dic13⋊C3), C2×C25×C3⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 18);