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C3×C5×D229⋊C3 #35207295

order20610
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D229⋊C3
unambiguous semidirect productD229⋊(C32×C5)
unambiguous semidirect product(C229⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D229)⋊(C3×C5)
unambiguous semidirect product(C5×D229)⋊C32
unambiguous semidirect product(C3×C5×D229)⋊C3

Splittings

Fitting, socleC3×C5×C229 ⋊ C2×C3
derived, SylowC229 ⋊ C2×C32×C5
HallC3×C5×C229⋊C3 ⋊ C2
HallC5×D229 ⋊ C32
HallC3×C229⋊C3 ⋊ C2×C5
HallC5×C229 ⋊ C2×C32
HallD229 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5D229⋊C3
commutator, cosocle, hypocenterC229C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C229C2×C3
LCSG ▷ C229
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3435

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20610, 14);