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C17×C3⋊(C31⋊AGL(1,𝔽5)) #44539363

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

Aliases

direct productC17×C3⋊(C31⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C17×C31⋊AGL(1,𝔽5))
unambiguous semidirect productC31⋊(C17×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, HallC3×C5×C31 ⋊ C4×C17
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC17×C31 ⋊ ΓL(1,𝔽16)
HallC3×C5×C17 ⋊ Dic31
HallC5×C31 ⋊ Dic3×C17
HallC3×C31 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ Dic93
HallC3×C17 ⋊ C31⋊AGL(1,𝔽5)
SylowC31 ⋊ C17×ΓL(1,𝔽16)
HallC3×C5 ⋊ C17×Dic31
SylowC5 ⋊ C17×Dic93
SylowC3 ⋊ C17×C31⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC17C3⋊(C31⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C31C4×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleC3×D5×C31C2×C17
LCSG ▷ C3×C5×C31
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 120);