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C3×C31×D205 #49185756

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31×D205
unambiguous semidirect productC5⋊(C3×C31×D41)
unambiguous semidirect productC41⋊(C3×D5×C31)

Splittings

Fitting, socle, HallC3×C5×C31×C41 ⋊ C2
derived, HallC5×C41 ⋊ C2×C3×C31
HallC5×C31×C41 ⋊ C2×C3
HallC3×C31×C41 ⋊ D5
HallC31×C41 ⋊ C3×D5
HallC3×C5×C41 ⋊ C2×C31
HallC3×C5×C31 ⋊ D41
HallC5×C31 ⋊ C3×D41
HallC3×C41 ⋊ D5×C31
SylowC41 ⋊ C3×D5×C31
HallC3×C5 ⋊ C31×D41
SylowC5 ⋊ C3×C31×D41

Subgroups

subgroupG/H
center, hypercenterC3×C31D205
commutator, cosocle, hypocenterC5×C41C2×C3×C31
FrattiniC1G
Fitting, socleC3×C5×C31×C41C2
LCSG ▷ C5×C41
UCSC1 ◁ C3×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19065

Conjugacy classes & character table

9672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 19);