Finite Group Databasebeta

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C5×C3⋊(C31⋊#595) #44539356

order31620
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C31⋊#595)
unambiguous semidirect productC3⋊(C5×C31⋊#595)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC3×C17×C31 ⋊ C4×C5
HallC5×C17×C31 ⋊ Dic3
HallC17×C31 ⋊ C5×Dic3
HallC3×C5×C31 ⋊ #595
HallC3×C5×C17 ⋊ Dic31
HallC5×C31 ⋊ C3⋊#595
HallC3×C31 ⋊ C5×#595
HallC5×C17 ⋊ Dic93
HallC3×C17 ⋊ C5×Dic31
SylowC31 ⋊ C5×C3⋊#595
SylowC17 ⋊ C5×Dic93
HallC3×C5 ⋊ C31⋊#595
SylowC3 ⋊ C5×C31⋊#595

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C31⋊#595)
commutator, hypocenterC3×C17×C31C4×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×C5×C31×D17C2
cosocleC3×C31×D17C2×C5
LCSG ▷ C3×C17×C31
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 113);