Finite Group Databasebeta

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C2×C3×C17×D31⋊C5 #44539320

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C17×D31⋊C5
unambiguous semidirect product(C2×C3×D31)⋊(C5×C17)
unambiguous semidirect product(C2×C3×C17×D31)⋊C5

Splittings

Fitting, socleC2×C3×C17×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C3×C5×C17
HallC3×C17×ΓL(1,𝔽32) ⋊ C22
HallC2×C3×C17×D31 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C17×D31 ⋊ C3×C5
HallC3×C17×C31 ⋊ C22×C5
HallC17×C31 ⋊ C22×C3×C5
HallC3×ΓL(1,𝔽32) ⋊ C22×C17
HallC2×C3×D31 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C22×C3×C17
HallC2×D31 ⋊ C3×C5×C17
HallC3×C31 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D31⋊C5
commutator, cosocle, hypocenterC31C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C17×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3162

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 77);