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C2×C3×C3⋊(D31⋊C5) #19150125

order5580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊(D31⋊C5)
unambiguous semidirect product(C2×C3)⋊(C3×D31⋊C5)
unambiguous semidirect product(C2×C3×D93)⋊C5

Splittings

Fitting, socleC2×C32×C31 ⋊ C2×C5
derivedC3×C31 ⋊ C22×C3×C5
HallC32×ΓL(1,𝔽32) ⋊ C22
HallC2×C3×D93 ⋊ C5
HallC32×C31 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×C3×D3
SylowC31 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D31⋊C5)
commutator, hypocenterC3×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×C3⋊(D31⋊C5), C2×C3×C5×C3⋊(D31⋊C5), C2×C3×C3⋊(C5⋊(D31⋊C5))
maximal normal subgroup ofC2×C3×C5×C3⋊(D31⋊C5)
maximal quotient ofC2×C3×C3⋊(D31⋊C25), C3×D5×C3⋊(D31⋊C5), C2×C3×C5×C3⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 114);