Finite Group Databasebeta

← Prev (#30655138) Next (#30655140) →

C7×C9⋊#63118 #30655139

order16380
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9⋊#63118
unambiguous semidirect productC9⋊(C7×#63118)

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C4
derived, HallC5×C9×C13 ⋊ C4×C7
HallC7×C9×C13 ⋊ Dic5
HallC5×C7×C13 ⋊ Dic9
HallC5×C7×C9 ⋊ #261
HallC9×C13 ⋊ C7×Dic5
HallC7×C13 ⋊ Dic45
HallC5×C13 ⋊ C7×Dic9
HallC7×C9 ⋊ #63118
HallC5×C9 ⋊ C7×#261
HallC5×C7 ⋊ C9⋊#261
SylowC13 ⋊ C7×Dic45
SylowC9 ⋊ C7×#63118
SylowC5 ⋊ C7×C9⋊#261

Subgroups

subgroupG/H
center, hypercenterC7C9⋊#63118
commutator, hypocenterC5×C9×C13C4×C7
FrattiniC3C7×C3⋊#63118
FittingC5×C7×C9×C13C4
socleC3×C5×C7×C13Dic3
prime radicalC3×C5×C7×D13D3
cosocleC5×C9×D13C2×C7
LCSG ▷ C5×C9×C13
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 189);