Finite Group Databasebeta

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C3×Dic5×#63271 #30655220

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

Aliases

direct productC3×Dic5×#63271

Splittings

derived, HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×#63271 ⋊ C4
HallC7×C13×Dic5 ⋊ C32
HallC13×Dic5 ⋊ C3×ΓL(1,𝔽8)
HallC7×Dic5 ⋊ C3×C13⋊C3
HallC7×C13 ⋊ C32×Dic5
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C3×Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×Dic5×C13⋊C3
SylowC5 ⋊ C3×C4×#63271

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×#63271
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC2C3×D5×#63271
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×#63271C2
cosocleC2×C5×C7×C13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 270);