Finite Group Databasebeta

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C3×#19129778 #30655380

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

Aliases

direct productC3×#19129778

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC7⋊#63118 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ Dic5
HallC3×C5×C13⋊C3 ⋊ Dic7
HallC3×C13⋊C3 ⋊ Dic35
HallC7×C13 ⋊ C32×Dic5
HallC5×C13 ⋊ C32×Dic7
HallC5×C7 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C32×Dic35
SylowC7 ⋊ C3×#63118⋊C3
SylowC5 ⋊ C3×#11763979

Subgroups

subgroupG/H
center, hypercenterC3#19129778
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13⋊C3C2
cosocleC5×C7×D13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 430);