Finite Group Databasebeta

← Prev (#20269170) Next (#20269172) →

C3×C5×C22⋊(C37⋊C3) #20269171

order6660
isoclinismisoclinic class of C22⋊(C37⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C22⋊(C37⋊C3)
unambiguous semidirect product(C22×C3)⋊(C5×C37⋊C3)
unambiguous semidirect product(C22×C3×C5)⋊(C37⋊C3)
unambiguous semidirect product(C3×C37)⋊(C5×A4)
unambiguous semidirect product(C3×C5×C37)⋊A4

Splittings

Fitting, socleC22×C3×C5×C37 ⋊ C3
derived, HallC22×C37 ⋊ C32×C5
HallC22×C5×C37 ⋊ C32
HallC5×C37 ⋊ C3×A4
SylowC37 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C37⋊C3
SylowC22 ⋊ C3×C5×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C37⋊C3)
commutator, hypocenterC22×C37C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C37C3
LCSG ▷ C22×C37
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C25×C22⋊(C37⋊C3), C3×C52×C22⋊(C37⋊C3)
maximal normal subgroup ofC3×C25×C22⋊(C37⋊C3), C3×C52×C22⋊(C37⋊C3)
maximal quotient ofC3×C25×C22⋊(C37⋊C3), C3×C52×C22⋊(C37⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 168);