Finite Group Databasebeta

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C2×C5×C13×D37⋊C3 #43274285

order28860
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D37⋊C3
unambiguous semidirect productD37⋊(C2×C3×C5×C13)
unambiguous semidirect product(C37⋊C3)⋊(C22×C5×C13)
unambiguous semidirect product(C2×D37)⋊(C3×C5×C13)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C5×C13)
unambiguous semidirect product(C2×C5×D37)⋊(C3×C13)

Splittings

Fitting, socleC2×C5×C13×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C3×C5×C13
HallC2×C5×C13×D37 ⋊ C3
HallC5×C13×C37⋊C3 ⋊ C22
HallC5×C13×C37 ⋊ C22×C3
HallC2×C13×D37 ⋊ C3×C5
HallC13×C37⋊C3 ⋊ C22×C5
HallC2×C5×D37 ⋊ C3×C13
HallC5×C37⋊C3 ⋊ C22×C13
HallC13×C37 ⋊ C22×C3×C5
HallC5×C37 ⋊ C22×C3×C13
HallC2×D37 ⋊ C3×C5×C13
HallC37⋊C3 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D37⋊C3
commutator, cosocle, hypocenterC37C22×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C5×C13×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4810

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 190);