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C5×(C139⋊C3)⋊D7 #44415919

order29190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C139⋊C3)⋊D7
unambiguous semidirect product(C139⋊C3)⋊(C5×D7)

Splittings

Fitting, socle, HallC5×C7×C139 ⋊ C2×C3
derived, HallC7×C139 ⋊ C2×C3×C5
HallC5×C7×C139⋊C3 ⋊ C2
HallC5×D973 ⋊ C3
HallC7×C139⋊C3 ⋊ C2×C5
HallC5×C139⋊C3 ⋊ D7
HallD973 ⋊ C3×C5
HallC5×C139 ⋊ C3×D7
HallC139⋊C3 ⋊ C5×D7
SylowC139 ⋊ C3×C5×D7
HallC5×C7 ⋊ D139⋊C3
SylowC7 ⋊ C5×D139⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C139⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C139C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C139C2×C3
LCSG ▷ C7×C139
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4865

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29190, 29);