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C3×C4⋊#4223 #14520187

order1968
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4⋊#4223
unambiguous semidirect productC4⋊(C3×#4223)

Splittings

FittingC3×C4×C41 ⋊ C4
HallC3×C41 ⋊ C4⋊C4
SylowC41 ⋊ C3×C4⋊C4

Subgroups

subgroupG/H
centerC2×C3C2×#4223
commutatorC2×C41C2×C3×C4
FrattiniC2C2×C3×#4223
FittingC3×C4×C41C4
socleC2×C3×C41C2×C4
prime radicalC2×C3×D41C22
cosocleC2×D41C22×C3
hypercenterC3×C4#4223
hypocenterC41C3×C4⋊C4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C3 ◁ C3×C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 492

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 110);