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C3×#27163263 #49185772

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#27163263

Splittings

Fitting, socle, HallC3×C31×C41 ⋊ C2×C5
derived, HallC31×C41 ⋊ C2×C3×C5
HallC3×#20263756 ⋊ C2
HallC3×C31×D41 ⋊ C5
Hall#20263756 ⋊ C2×C3
HallC31×D41 ⋊ C3×C5
HallC3×D41 ⋊ ΓL(1,𝔽32)
HallC3×C41 ⋊ C2×ΓL(1,𝔽32)
HallC3×C31 ⋊ D41⋊C5
HallD41 ⋊ C3×ΓL(1,𝔽32)
SylowC41 ⋊ C2×C3×ΓL(1,𝔽32)
SylowC31 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#27163263
commutator, cosocle, hypocenterC31×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C31×C41C2×C5
LCSG ▷ C31×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3813

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 35);