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C2×C3×C31×D65 #37564004

order24180
automorphism?
homologyAbelianization (H1) = C22×C3×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C31×D65
unambiguous semidirect product(C2×C5)⋊(C3×D13×C31)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC5×C13 ⋊ C22×C3×C31
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C22×C3
HallC3×C13×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×C3×D5
HallC3×C5×C13 ⋊ C22×C31
HallC5×C31 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×D5×C31
HallC3×C5 ⋊ C2×D13×C31
SylowC13 ⋊ C2×C3×D5×C31
SylowC5 ⋊ C2×C3×D13×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D65
commutator, cosocle, hypocenterC5×C13C22×C3×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

6324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 303);