Finite Group Databasebeta

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C3×C5×C22⋊#87704 #37561623

order23940
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C22⋊#87704
unambiguous semidirect product(C22×C3)⋊(C5×#87704)
unambiguous semidirect product(C22×C3×C5)⋊#87704

Splittings

Fitting, socleC22×C3×C5×C7×C19 ⋊ C3
derived, HallC22×C7×C19 ⋊ C32×C5
HallC22×C5×C7×C19 ⋊ C32
HallC5×C7×C19 ⋊ C3×A4
HallC22×C5×C19 ⋊ C3×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C3×C19⋊C3
HallC7×C19 ⋊ C3×C5×A4
HallC5×C19 ⋊ C3×C22⋊ΓL(1,𝔽8)
HallC22×C19 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C22⋊(C19⋊C3)
HallC22×C7 ⋊ C3×C5×C19⋊C3
HallC22×C5 ⋊ C3×#87704
SylowC19 ⋊ C3×C5×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×C22⋊(C19⋊C3)
SylowC22 ⋊ C3×C5×#87704

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊#87704
commutator, cosocle, hypocenterC22×C7×C19C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C7×C19C3
LCSG ▷ C22×C7×C19
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 755);