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C4×C17×(C31⋊C3)⋊C5 #44539247

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×(C31⋊C3)⋊C5
unambiguous semidirect product(C4×C31⋊C3)⋊(C5×C17)
unambiguous semidirect product(C4×ΓL(1,𝔽32))⋊(C3×C17)
unambiguous semidirect product(C4×C17×C31⋊C3)⋊C5
unambiguous semidirect product(C4×C17×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, HallC4×C17×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C3×C4×C5×C17
HallC4×C17×ΓL(1,𝔽32) ⋊ C3
HallC4×C17×C31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallC17×C31⋊C3 ⋊ C4×C5
HallC4×ΓL(1,𝔽32) ⋊ C3×C17
HallC17×C31 ⋊ C3×C4×C5
HallC4×C31⋊C3 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C3×C4×C17
HallC4×C31 ⋊ C3×C5×C17
HallC31⋊C3 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17(C31⋊C3)⋊C5
commutator, hypocenterC31C3×C4×C5×C17
FrattiniC2C2×C17×(C31⋊C3)⋊C5
FittingC4×C17×C31C3×C5
socleC2×C17×C31C2×C3×C5
prime radicalC2×C17×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C4×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 4);