Finite Group Databasebeta

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C3×C4×C5×#63270 #30655258

order16380
isoclinismisoclinic class of #63270
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C5×#63270

Splittings

FittingC3×C4×C5×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C32×C4×C5
HallC4×C5×C7×C13 ⋊ C32
HallC5×C7×C13 ⋊ C32×C4
HallC4×C7×C13 ⋊ C32×C5
HallC4×C5×C13 ⋊ C3×ΓL(1,𝔽8)
HallC4×C5×C7 ⋊ C3×C13⋊C3
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallC4×C13 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C4×C13⋊C3
HallC4×C7 ⋊ C3×C5×C13⋊C3
SylowC13 ⋊ C3×C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C4×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5#63270
commutator, hypocenterC7×C13C32×C4×C5
FrattiniC2C2×C3×C5×#63270
FittingC3×C4×C5×C7×C13C3
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×#63270C2
cosocleC2×C7×C13C2×C32×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C4×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 308);