Finite Group Databasebeta

← Prev (#36345298) Next (#36345300) →

C3×C5×C3⋊#92150 #36345299

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productC3×C5×C3⋊#92150
unambiguous semidirect productC3⋊(C3×C5×#92150)

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C4
derivedC3×C112 ⋊ C3×C4×C5
HallC32×C112 ⋊ C4×C5
HallC5×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×C5×Dic3
HallC32×C5 ⋊ #92150
SylowC32 ⋊ C5×#92150

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#92150
commutator, hypocenterC3×C112C3×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C112C4
prime radicalC32×C5×C11⋊D11C2
cosocleC3×C11⋊D11C2×C3×C5
LCSG ▷ C3×C112
UCSC1 ◁ C3×C5

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 648);