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C22×C3×C17×ΓL(1,𝔽32) #44539334

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

Aliases

direct productC22×C3×C17×ΓL(1,𝔽32)
unambiguous semidirect product(C22×C3×C31)⋊(C5×C17)
unambiguous semidirect product(C22×C3×C17×C31)⋊C5

Splittings

Fitting, socle, HallC22×C3×C17×C31 ⋊ C5
derived, SylowC31 ⋊ C22×C3×C5×C17
HallC22×C17×C31 ⋊ C3×C5
HallC3×C17×C31 ⋊ C22×C5
HallC17×C31 ⋊ C22×C3×C5
HallC22×C3×C31 ⋊ C5×C17
HallC22×C31 ⋊ C3×C5×C17
HallC3×C31 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC22×C3×C17ΓL(1,𝔽32)
commutator, cosocle, hypocenterC31C22×C3×C5×C17
FrattiniC1G
Fitting, socleC22×C3×C17×C31C5
LCSG ▷ C31
UCSC1 ◁ C22×C3×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6324

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 91);