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C3×C3⋊(C5⋊(D31⋊C5)) #28358465

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C5⋊(D31⋊C5))
unambiguous semidirect productC3⋊(C3×C5⋊(D31⋊C5))
unambiguous semidirect productC5⋊(C3×C3⋊(D31⋊C5))
unambiguous semidirect product(C3×D465)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C2×C5
derivedC3×C5×C31 ⋊ C2×C3×C5
HallC32×C5×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C3×D3
HallC32×C31 ⋊ C5×D5
SylowC31 ⋊ C3×C5×D15
SylowC32 ⋊ C5⋊(D31⋊C5)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C5⋊(D31⋊C5))
commutator, cosocle, hypocenterC3×C5×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C31C2×C5
LCSG ▷ C3×C5×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D15×D31⋊C5, C3×D5×C3⋊(D31⋊C5), C3×D3×C5⋊(D31⋊C5), …
maximal normal subgroup ofC3×D15×D31⋊C5, C3×D5×C3⋊(D31⋊C5), C3×D3×C5⋊(D31⋊C5), …
maximal quotient ofC3×C3⋊(ΓL(1,𝔽32)⋊Dic5), C2×C3×C3⋊(C5⋊(D31⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 108);