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C3×C4×C5×C31⋊C3 #19150085

order5580
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C5×C31⋊C3
unambiguous semidirect product(C4×C5×C31)⋊C32
unambiguous semidirect product(C3×C4×C5×C31)⋊C3

Splittings

FittingC3×C4×C5×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C4×C5
HallC4×C5×C31 ⋊ C32
HallC5×C31 ⋊ C32×C4
HallC4×C31 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C31⋊C3
commutator, hypocenterC31C32×C4×C5
FrattiniC2C2×C3×C5×C31⋊C3
FittingC3×C4×C5×C31C3
socleC2×C3×C5×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C3×C4×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×(C31⋊C3)⋊C25, C3×C4×C25×C31⋊C3, C3×C4×C5×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC3×C4×(C31⋊C3)⋊C25, C3×C4×C25×C31⋊C3, C3×C4×C5×(C31⋊C3)⋊C5, …
maximal quotient ofC3×C4×C25×C31⋊C3, C3×C5×Dic5×C31⋊C3, C3×C4×C52×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 74);