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C17×C31×ΓL(1,𝔽16) #44539362

order31620
automorphism?
homologyAbelianization (H1) = C4×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC17×C31×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C17×AGL(1,𝔽5)×C31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC3×C5 ⋊ C4×C17×C31
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC3×C5×C31 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C31
HallC5×C31 ⋊ Dic3×C17
HallC3×C31 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ Dic3×C31
HallC3×C17 ⋊ AGL(1,𝔽5)×C31
SylowC5 ⋊ Dic3×C17×C31
SylowC3 ⋊ C17×AGL(1,𝔽5)×C31

Subgroups

subgroupG/H
center, hypercenterC17×C31ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C17×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleC3×D5C2×C17×C31
LCSG ▷ C3×C5
UCSC1 ◁ C17×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

4743 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 119);