Finite Group Databasebeta

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C3×C5×C31⋊#595 #44539336

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C31⋊#595

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5C31⋊#595
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×C5×C31×D17C2
cosocleC31×D17C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

2370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 93);