Finite Group Databasebeta

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C2×C5×D3×C139⋊C3 #38736256

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

Aliases

direct productC2×C5×D3×C139⋊C3
unambiguous semidirect productC3⋊(C22×C5×C139⋊C3)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C139⋊C3)
unambiguous semidirect product(C2×D3×C139)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D3×C139)⋊C3

Splittings

Fitting, socleC2×C3×C5×C139 ⋊ C2×C3
derivedC3×C139 ⋊ C22×C3×C5
HallC3×C5×C139⋊C3 ⋊ C22
HallC3×C139⋊C3 ⋊ C22×C5
HallC5×C139 ⋊ C2×C3×D3
SylowC139 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×C139⋊C3
commutator, cosocle, hypocenterC3×C139C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C139C2×C3
LCSG ▷ C3×C139
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4170

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25020, 78);