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C3×C5⋊#13049954 #34086245

order19530
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊#13049954
unambiguous semidirect productC5⋊(C3×#13049954)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derived, HallC5×C7×C31 ⋊ C2×C32
HallC3×C5×#10620252 ⋊ C2
HallC7×D155 ⋊ C32
HallC3×#10620252 ⋊ D5
HallD155 ⋊ C3×ΓL(1,𝔽8)
HallC7×C31 ⋊ C32×D5
HallC5×C31 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D31⋊C3
SylowC31 ⋊ C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5⋊(D31⋊C3)
SylowC5 ⋊ C3×#13049954

Subgroups

subgroupG/H
center, hypercenterC3C5⋊#13049954
commutator, cosocle, hypocenterC5×C7×C31C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C5×C7×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 150);