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C2×C3×C5⋊(D157⋊C3) #43246341

order28260
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5⋊(D157⋊C3)
unambiguous semidirect product(C2×C5)⋊(C3×D157⋊C3)
unambiguous semidirect product(C2×C157⋊C3)⋊(C3×D5)
unambiguous semidirect product(C2×D785)⋊C32
unambiguous semidirect product(C2×C3×D785)⋊C3

Splittings

Fitting, socleC2×C3×C5×C157 ⋊ C2×C3
derived, HallC5×C157 ⋊ C22×C32
HallC3×C5×C157⋊C3 ⋊ C22
HallC2×D785 ⋊ C32
HallC3×C157⋊C3 ⋊ C2×D5
SylowC157 ⋊ C2×C32×D5
SylowC5 ⋊ C2×C3×D157⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D157⋊C3)
commutator, cosocle, hypocenterC5×C157C22×C32
FrattiniC1G
Fitting, socleC2×C3×C5×C157C2×C3
LCSG ▷ C5×C157
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4710

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28260, 95);