Finite Group Databasebeta

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C3×C31×#66774 #44539344

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31×#66774

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC5×C17 ⋊ C3×C4×C31
HallC5×C17×C31 ⋊ C3×C4
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC17×C31 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C31 ⋊ Dic17
HallC3×C5×C17 ⋊ C4×C31
HallC5×C31 ⋊ C3×Dic17
HallC3×C17 ⋊ AGL(1,𝔽5)×C31
SylowC17 ⋊ C3×AGL(1,𝔽5)×C31
HallC3×C5 ⋊ C31×Dic17
SylowC5 ⋊ C3×C31×Dic17

Subgroups

subgroupG/H
center, hypercenterC3×C31#66774
commutator, hypocenterC5×C17C3×C4×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleD5×C17C2×C3×C31
LCSG ▷ C5×C17
UCSC1 ◁ C3×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3441 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 101);