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Dic3×2−1+4⋊C3 #11923395

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productDic3×2−1+4⋊C3
unambiguous semidirect product(Dic3×2−1+4)⋊C3

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FittingC2×C3×2−1+4C2×C3
socleC22×C3C23×A4
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC2×C3×Q8C23×C3
hypercenterC2×D4D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×D4

787 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 137 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) = 192

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157406);