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C2×C3×C41×D65 #44544491

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C41×D65
unambiguous semidirect product(C2×C5)⋊(C3×D13×C41)

Splittings

Fitting, socleC2×C3×C5×C13×C41 ⋊ C2
derived, HallC5×C13 ⋊ C22×C3×C41
HallC3×C5×C13×C41 ⋊ C22
HallC5×C13×C41 ⋊ C22×C3
HallC3×C13×C41 ⋊ C2×D5
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×C3×D5
HallC5×C41 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C22×C41
HallC3×C13 ⋊ C2×D5×C41
HallC3×C5 ⋊ C2×D13×C41
SylowC13 ⋊ C2×C3×D5×C41
SylowC5 ⋊ C2×C3×D13×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C41D65
commutator, cosocle, hypocenterC5×C13C22×C3×C41
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C41C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C41

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15990

Conjugacy classes & character table

8364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 219);