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C3×#19129729 #30655331

order16380
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×#19129729

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×#63270 ⋊ C4
HallC7⋊#63120 ⋊ C32
HallC3×#63270 ⋊ AGL(1,𝔽5)
HallC7×C13 ⋊ C32×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×Dic13⋊C3
SylowC13 ⋊ C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
SylowC7 ⋊ C3×#63120⋊C3
SylowC5 ⋊ C3×#11763963

Subgroups

subgroupG/H
center, hypercenterC3#19129729
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×D5×#63270C2
cosocleC7×D5×C13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 381);