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C3×C17×C31⋊AGL(1,𝔽5) #44539339

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×C31⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC5×C31 ⋊ C3×C4×C17
HallC5×C17×C31 ⋊ C3×C4
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC17×C31 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C31 ⋊ C4×C17
HallC3×C5×C17 ⋊ Dic31
HallC3×C31 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ C3×Dic31
SylowC31 ⋊ C3×C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×Dic31
SylowC5 ⋊ C3×C17×Dic31

Subgroups

subgroupG/H
center, hypercenterC3×C17C31⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C3×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleD5×C31C2×C3×C17
LCSG ▷ C5×C31
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3315 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 96);