Finite Group Databasebeta

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C4×C5×#13183715 #47977533

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#13183715

Splittings

Fitting, HallC4×C5×C19×C31 ⋊ C3
derived, HallC19×C31 ⋊ C3×C4×C5
HallC5×C19×C31 ⋊ C3×C4
HallC4×C19×C31 ⋊ C3×C5
HallC4×C5×C31 ⋊ C19⋊C3
HallC4×C5×C19 ⋊ C31⋊C3
HallC5×C31 ⋊ C4×C19⋊C3
HallC4×C31 ⋊ C5×C19⋊C3
HallC5×C19 ⋊ C4×C31⋊C3
HallC4×C19 ⋊ C5×C31⋊C3
SylowC31 ⋊ C4×C5×C19⋊C3
SylowC19 ⋊ C4×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#13183715
commutator, hypocenterC19×C31C3×C4×C5
FrattiniC2C2×C5×#13183715
FittingC4×C5×C19×C31C3
socleC2×C5×C19×C31C2×C3
prime radicalC2×C5×#13183715C2
cosocleC2×C19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11780

Conjugacy classes & character table

3980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 5);