Finite Group Databasebeta

← Prev (#44479190) Next (#44479192) →

C3×C3⋊(C7⋊#92150) #44479191

order30492
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productC3×C3⋊(C7⋊#92150)
unambiguous semidirect productC3⋊(C3×C7⋊#92150)

Splittings

Fitting, socle, HallC32×C7×C112 ⋊ C4
derivedC3×C7×C112 ⋊ C3×C4
HallC32×C112 ⋊ Dic7
HallC7×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×Dic21
HallC32×C7 ⋊ #92150
SylowC32 ⋊ C7⋊#92150
SylowC7 ⋊ C3×C3⋊#92150

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C7⋊#92150)
commutator, hypocenterC3×C7×C112C3×C4
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC32×C7×C11⋊D11C2
cosocleC3×C7×C11⋊D11C2×C3
LCSG ▷ C3×C7×C112
UCSC1 ◁ C3

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

1962 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 414);