Finite Group Databasebeta

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C2×C5×C37×D13⋊C3 #43274286

order28860
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C37×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C5×C37)
unambiguous semidirect product(C13⋊C3)⋊(C22×C5×C37)
unambiguous semidirect product(C2×D13)⋊(C3×C5×C37)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C5×C37)
unambiguous semidirect product(C2×C5×D13)⋊(C3×C37)

Splittings

Fitting, socleC2×C5×C13×C37 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C5×C37
HallC2×C5×D13×C37 ⋊ C3
HallC5×C37×C13⋊C3 ⋊ C22
HallC5×C13×C37 ⋊ C22×C3
HallC2×D13×C37 ⋊ C3×C5
HallC37×C13⋊C3 ⋊ C22×C5
HallC13×C37 ⋊ C22×C3×C5
HallC2×C5×D13 ⋊ C3×C37
HallC5×C13⋊C3 ⋊ C22×C37
HallC5×C13 ⋊ C22×C3×C37
HallC2×D13 ⋊ C3×C5×C37
HallC13⋊C3 ⋊ C22×C5×C37

Subgroups

subgroupG/H
center, hypercenterC2×C5×C37D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C5×C37
FrattiniC1G
Fitting, socleC2×C5×C13×C37C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4810

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 191);