Finite Group Databasebeta

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C31×C3⋊#66774 #44539368

order31620
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×C3⋊#66774
unambiguous semidirect productC3⋊(C31×#66774)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C31
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC17×C31 ⋊ ΓL(1,𝔽16)
HallC3×C5×C31 ⋊ Dic17
HallC5×C31 ⋊ Dic51
HallC3×C31 ⋊ #66774
HallC5×C17 ⋊ Dic3×C31
HallC3×C17 ⋊ AGL(1,𝔽5)×C31
SylowC17 ⋊ C31×ΓL(1,𝔽16)
HallC3×C5 ⋊ C31×Dic17
SylowC5 ⋊ C31×Dic51
SylowC3 ⋊ C31×#66774

Subgroups

subgroupG/H
center, hypercenterC31C3⋊#66774
commutator, hypocenterC3×C5×C17C4×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleC3×D5×C17C2×C31
LCSG ▷ C3×C5×C17
UCSC1 ◁ C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3255 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 125);