Finite Group Databasebeta

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C5×C3⋊(C3⋊(C7⋊#261)) #30655676

order16380
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊(C3⋊(C7⋊#261))
unambiguous semidirect productC3⋊(C5×C3⋊(C7⋊#261))
unambiguous semidirect productC7⋊(C5×C3⋊(C3⋊#261))

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C7×C13 ⋊ C4×C5
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ #261
HallC32×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ C5×C3⋊Dic3
HallC5×C13 ⋊ C3⋊Dic21
HallC32×C7 ⋊ C5×#261
HallC32×C5 ⋊ C7⋊#261
HallC5×C7 ⋊ C3⋊(C3⋊#261)
SylowC13 ⋊ C5×C3⋊Dic21
SylowC32 ⋊ C5×C7⋊#261
SylowC7 ⋊ C5×C3⋊(C3⋊#261)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(C7⋊#261))
commutator, hypocenterC32×C7×C13C4×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C5×C7×D13C2
cosocleC32×C7×D13C2×C5
LCSG ▷ C32×C7×C13
UCSC1 ◁ C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 726);