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C3×C3⋊(Dic31⋊C5) #19150073

order5580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic31⋊C5)
unambiguous semidirect productC3⋊(C3×Dic31⋊C5)
unambiguous semidirect product(C3×Dic93)⋊C5

Splittings

derivedC3×C31 ⋊ C3×C4×C5
HallC32×ΓL(1,𝔽32) ⋊ C4
HallC3×Dic93 ⋊ C5
HallC32×C31 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C3×Dic3
SylowC31 ⋊ C3×C5×Dic3
SylowC32 ⋊ Dic31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D31⋊C5)
commutator, hypocenterC3×C31C3×C4×C5
FrattiniC2C3×C3⋊(D31⋊C5)
Fitting, socleC2×C32×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C3⋊(Dic31⋊C5), C3×C3⋊(ΓL(1,𝔽32)⋊Dic5), C3×C3⋊(ΓL(1,𝔽32)⋊AGL(1,𝔽5))
maximal normal subgroup ofC3×C5×C3⋊(Dic31⋊C5)
maximal quotient ofC3×C3⋊(Dic31⋊C25), C3×C5×C3⋊(Dic31⋊C5), C3×C3⋊(ΓL(1,𝔽32)⋊Dic5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 62);