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C2×C3×C5×D139⋊C3 #38736252

order25020
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×D139⋊C3
unambiguous semidirect productD139⋊(C2×C32×C5)
unambiguous semidirect product(C139⋊C3)⋊(C22×C3×C5)
unambiguous semidirect product(C2×D139)⋊(C32×C5)
unambiguous semidirect product(C2×C139⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D139)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D139)⋊C32
unambiguous semidirect product(C2×C3×C5×D139)⋊C3

Splittings

Fitting, socleC2×C3×C5×C139 ⋊ C2×C3
derived, SylowC139 ⋊ C22×C32×C5
HallC3×C5×C139⋊C3 ⋊ C22
HallC2×C5×D139 ⋊ C32
HallC3×C139⋊C3 ⋊ C22×C5
HallC5×C139 ⋊ C22×C32
HallC2×D139 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D139⋊C3
commutator, cosocle, hypocenterC139C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C139C2×C3
LCSG ▷ C139
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4170

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25020, 74);