Finite Group Databasebeta

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C5×C7×C3⋊(C3⋊#261) #30655674

order16380
isoclinismisoclinic class of C3⋊(C3⋊#261)
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C3⋊(C3⋊#261)
unambiguous semidirect productC3⋊(C5×C7×C3⋊#261)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C13 ⋊ C4×C5×C7
HallC32×C7×C13 ⋊ C4×C5
HallC32×C5×C13 ⋊ C4×C7
HallC5×C7×C13 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ #261
HallC7×C13 ⋊ C5×C3⋊Dic3
HallC5×C13 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C5×#261
HallC32×C5 ⋊ C7×#261
SylowC13 ⋊ C5×C7×C3⋊Dic3
SylowC32 ⋊ C5×C7×#261

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C5×C7×D13C2
cosocleC32×D13C2×C5×C7
LCSG ▷ C32×C13
UCSC1 ◁ C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 724);