Finite Group Databasebeta

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C2×C3×D13⋊C3×C79 #49149584

order36972
automorphism?
homologyAbelianization (H1) = C22×C32×C79 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D13⋊C3×C79
unambiguous semidirect productD13⋊(C2×C32×C79)
unambiguous semidirect product(C13⋊C3)⋊(C22×C3×C79)
unambiguous semidirect product(C2×D13)⋊(C32×C79)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C3×C79)
unambiguous semidirect product(C2×C3×D13)⋊(C3×C79)

Splittings

Fitting, socleC2×C3×C13×C79 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C32×C79
HallC3×C13⋊C3×C79 ⋊ C22
HallC2×D13×C79 ⋊ C32
HallC13×C79 ⋊ C22×C32
HallC3×C13⋊C3 ⋊ C22×C79
HallC2×D13 ⋊ C32×C79

Subgroups

subgroupG/H
center, hypercenterC2×C3×C79D13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C79
FrattiniC1G
Fitting, socleC2×C3×C13×C79C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C79

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6162

Conjugacy classes & character table

3792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 232);