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C3×C5×#13049955 #34086232

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×#13049955

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C32×C5
HallC3×C5×#10620253 ⋊ C2
HallC5×C7×D31 ⋊ C32
HallC3×#10620253 ⋊ C2×C5
HallC5×C7×C31 ⋊ C2×C32
HallC7×D31 ⋊ C32×C5
HallC5×D31 ⋊ C3×ΓL(1,𝔽8)
HallC5×C31 ⋊ C2×C3×ΓL(1,𝔽8)
HallD31 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D31⋊C3
SylowC31 ⋊ C2×C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5#13049955
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C7×C31
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 137);