Finite Group Databasebeta

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C13×C7⋊#4379 #30655767

order16380
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C7⋊#4379
unambiguous semidirect productC7⋊(C13×#4379)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C5×C7 ⋊ C4×C13
HallC32×C7×C13 ⋊ Dic5
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ #157
HallC32×C13 ⋊ Dic35
HallC7×C13 ⋊ #4379
HallC5×C13 ⋊ C7⋊#157
HallC32×C7 ⋊ C13×Dic5
HallC32×C5 ⋊ C13×Dic7
HallC5×C7 ⋊ C13×#157
SylowC32 ⋊ C13×Dic35
SylowC7 ⋊ C13×#4379
SylowC5 ⋊ C13×C7⋊#157

Subgroups

subgroupG/H
center, hypercenterC13C7⋊#4379
commutator, hypocenterC32×C5×C7C4×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC5×C7×C13×C3⋊D3C2
cosocleC5×C7×C3⋊D3C2×C13
LCSG ▷ C32×C5×C7
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 817);