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C31×(C3⋊D3)⋊D5 #19150164

order5580
isoclinismisoclinic class of (C3⋊D3)⋊D5
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2

Aliases

direct productC31×(C3⋊D3)⋊D5
unambiguous semidirect product(C3⋊D3)⋊(D5×C31)
unambiguous semidirect productD15⋊(D3×C31)

Splittings

Fitting, socle, HallC32×C5×C31 ⋊ C22
derived, HallC32×C5 ⋊ C22×C31
HallC32×C31 ⋊ C2×D5
HallC5×C31 ⋊ D32
SylowC32 ⋊ C2×D5×C31
SylowC5 ⋊ D32×C31

Subgroups

subgroupG/H
center, hypercenterC31(C3⋊D3)⋊D5
commutator, hypocenterC32×C5C22×C31
FrattiniC1G
Fitting, socleC32×C5×C31C22
LCSG ▷ C32×C5
UCSC1 ◁ C31

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

651 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31×(C3⋊D3)⋊D25, ΓL(1,𝔽32)×(C3⋊D3)⋊D5, C5×C31×(C3⋊D3)⋊D5, …
maximal normal subgroup ofΓL(1,𝔽32)×(C3⋊D3)⋊D5, C5×C31×(C3⋊D3)⋊D5
maximal quotient ofC31×(C3⋊D3)⋊D25, C5×C31×(C3⋊D3)⋊D5, C31×D15⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 153);