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SD16×C3⋊#170 #14286146

order1920
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productSD16×C3⋊#170

Splittings

HallC3×C5 ⋊ C8×SD16
SylowC5 ⋊ SD16×C3⋊C8
SylowC3 ⋊ SD16×#170

Subgroups

subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C22×C8
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D4C2×C4
cosocleC3×C4×Dic5C23
hypercenterC2×SD16ΓL(1,𝔽16)
hypocenterC3×C5C8×SD16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11844);