Finite Group Databasebeta

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C17×C3⋊(Dic31⋊C5) #44539267

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

Aliases

direct productC17×C3⋊(Dic31⋊C5)
unambiguous semidirect productC3⋊(C17×Dic31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(Dic3×C17)
unambiguous semidirect productDic93⋊(C5×C17)
unambiguous semidirect product(C17×Dic93)⋊C5

Splittings

derived, HallC3×C31 ⋊ C4×C5×C17
HallC3×C17×ΓL(1,𝔽32) ⋊ C4
HallC17×Dic93 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ Dic3
HallC3×C17×C31 ⋊ C4×C5
HallC17×C31 ⋊ C5×Dic3
HallC3×ΓL(1,𝔽32) ⋊ C4×C17
HallDic93 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ Dic3×C17
HallC3×C17 ⋊ Dic31⋊C5
SylowC31 ⋊ C5×Dic3×C17
SylowC3 ⋊ C17×Dic31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(D31⋊C5)
commutator, hypocenterC3×C31C4×C5×C17
FrattiniC2C17×C3⋊(D31⋊C5)
Fitting, socleC2×C3×C17×C31C2×C5
prime radicalC2×C3×C17×ΓL(1,𝔽32)C2
cosocleC2×C3×C31C2×C5×C17
LCSG ▷ C3×C31
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6324

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 24);