Finite Group Databasebeta

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C2×Dic6×3−1+2 #13048838

order1296
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic6×3−1+2
unambiguous semidirect product(C2×C3)⋊(Q8×3−1+2)
unambiguous semidirect product(C2×C9×Dic6)⋊C3

Splittings

SylowC3×3−1+2 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22×C3C2×C32×D3
commutator, cosocleC2×C32C23×C32
FrattiniC2×C3C22×C32×D3
FittingC2×C3×C4×3−1+2C2
socleC22×C32C22×C32
prime radicalC22×C33C22×C3
hypercenterC2×C4×3−1+2D3
hypocenterC3C2×Q8×3−1+2
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C4×3−1+2

392 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 189 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) = 144

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2556);