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C17×(C31⋊C3)⋊AGL(1,𝔽5) #44539304

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

Aliases

direct productC17×(C31⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C31⋊C3)⋊(C17×AGL(1,𝔽5))
unambiguous semidirect product(C31⋊AGL(1,𝔽5))⋊(C3×C17)
unambiguous semidirect product(C17×C31⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, HallC5×C17×C31 ⋊ C3×C4
derived, HallC5×C31 ⋊ C3×C4×C17
HallC17×C31⋊AGL(1,𝔽5) ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC17×C31⋊C3 ⋊ AGL(1,𝔽5)
HallC31⋊AGL(1,𝔽5) ⋊ C3×C17
HallC17×C31 ⋊ C3×AGL(1,𝔽5)
HallC5×C31⋊C3 ⋊ C4×C17
HallC31⋊C3 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C17×AGL(1,𝔽5)
SylowC5 ⋊ C17×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC17(C31⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C3×C4×C17
FrattiniC1G
Fitting, socleC5×C17×C31C3×C4
prime radicalD5×C17×C31⋊C3C2
cosocleD5×C31C2×C3×C17
LCSG ▷ C5×C31
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2635

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 61);