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C2×C17×D139⋊C3 #43248581

order28356
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D139⋊C3
unambiguous semidirect productD139⋊(C2×C3×C17)
unambiguous semidirect product(C139⋊C3)⋊(C22×C17)
unambiguous semidirect product(C2×D139)⋊(C3×C17)
unambiguous semidirect product(C2×C139⋊C3)⋊(C2×C17)
unambiguous semidirect product(C2×C17×D139)⋊C3

Splittings

Fitting, socleC2×C17×C139 ⋊ C2×C3
derived, SylowC139 ⋊ C22×C3×C17
HallC2×C17×D139 ⋊ C3
HallC17×C139⋊C3 ⋊ C22
HallC17×C139 ⋊ C22×C3
HallC2×D139 ⋊ C3×C17
HallC139⋊C3 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D139⋊C3
commutator, cosocle, hypocenterC139C22×C3×C17
FrattiniC1G
Fitting, socleC2×C17×C139C2×C3
LCSG ▷ C139
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4726

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28356, 17);