Finite Group Databasebeta

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C3×C41×D31⋊C5 #49185774

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×C41×D31⋊C5
unambiguous semidirect product(C3×D31)⋊(C5×C41)

Splittings

Fitting, socle, HallC3×C31×C41 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C3×C5×C41
HallC3×C41×ΓL(1,𝔽32) ⋊ C2
HallC3×C41×D31 ⋊ C5
HallC41×ΓL(1,𝔽32) ⋊ C2×C3
HallC41×D31 ⋊ C3×C5
HallC31×C41 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽32) ⋊ C2×C41
HallC3×D31 ⋊ C5×C41
HallΓL(1,𝔽32) ⋊ C2×C3×C41
HallC3×C31 ⋊ C2×C5×C41
HallD31 ⋊ C3×C5×C41

Subgroups

subgroupG/H
center, hypercenterC3×C41D31⋊C5
commutator, cosocle, hypocenterC31C2×C3×C5×C41
FrattiniC1G
Fitting, socleC3×C31×C41C2×C5
LCSG ▷ C31
UCSC1 ◁ C3×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3813

Conjugacy classes & character table

1599 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 37);