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C2×C3⋊#66243 #14514570

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

Aliases

direct productC2×C3⋊#66243
unambiguous semidirect product(C2×C3)⋊#66243

Splittings

SylowC3 ⋊ C2×#66243

Subgroups

subgroupG/H
center, hypercenterC22C3⋊((C24⋊C5)⋊C2)
commutator, cosocle, hypocenterC3×2−1+4⋊C5C22
FrattiniC2C2×C3⋊((C24⋊C5)⋊C2)
FittingC2×C3×2−1+4D5
socleC22×C3(C24⋊C5)⋊C2
prime radicalC2×C3×2−1+4⋊C5C2
LCSG ▷ C3×2−1+4⋊C5
UCSC1 ◁ C22

422 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240268);