Finite Group Databasebeta

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C22⋊C4×C3⋊#170 #14295159

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×C3⋊#170

Splittings

HallC3×C5 ⋊ C8×C22⋊C4
SylowC5 ⋊ C22⋊C4×C3⋊C8
SylowC3 ⋊ C22⋊C4×#170

Subgroups

subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5C8×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20857);