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C3×C5×(C139⋊C3)⋊C4 #38736220

order25020
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×(C139⋊C3)⋊C4
unambiguous semidirect product(C139⋊C3)⋊(C3×C4×C5)
unambiguous semidirect productDic139⋊(C32×C5)
unambiguous semidirect product(C3×Dic139)⋊(C3×C5)
unambiguous semidirect product(C5×Dic139)⋊C32
unambiguous semidirect product(C3×C5×Dic139)⋊C3

Splittings

derived, SylowC139 ⋊ C32×C4×C5
HallC3×C5×C139⋊C3 ⋊ C4
HallC5×Dic139 ⋊ C32
HallC3×C139⋊C3 ⋊ C4×C5
HallC5×C139 ⋊ C32×C4
HallDic139 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D139⋊C3
commutator, hypocenterC139C32×C4×C5
FrattiniC2C3×C5×D139⋊C3
Fitting, socleC2×C3×C5×C139C2×C3
prime radicalC2×C3×C5×C139⋊C3C2
cosocleC2×C139C2×C32×C5
LCSG ▷ C139
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8340

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, 42);