Finite Group Databasebeta

← Prev (#30655689) Next (#30655691) →

C7×C3⋊(C3⋊#63118) #30655690

order16380
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊(C3⋊#63118)
unambiguous semidirect productC3⋊(C7×C3⋊#63118)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C5×C13 ⋊ C4×C7
HallC32×C7×C13 ⋊ Dic5
HallC5×C7×C13 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ #261
HallC32×C13 ⋊ C7×Dic5
HallC7×C13 ⋊ C3⋊Dic15
HallC5×C13 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ #63118
HallC32×C5 ⋊ C7×#261
HallC5×C7 ⋊ C3⋊(C3⋊#261)
SylowC13 ⋊ C7×C3⋊Dic15
SylowC32 ⋊ C7×#63118
SylowC5 ⋊ C7×C3⋊(C3⋊#261)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊#63118)
commutator, hypocenterC32×C5×C13C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C5×C7×D13C2
cosocleC32×C5×D13C2×C7
LCSG ▷ C32×C5×C13
UCSC1 ◁ C7

144 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, 740);