Finite Group Databasebeta

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C22×Dic3×3−1+2 #13048878

order1296
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×Dic3×3−1+2

Splittings

SylowC3×3−1+2 ⋊ C22×C4

Subgroups

subgroupG/H
centerC23×C3C32×D3
commutatorC32C22×C32×C4
FrattiniC2×C3C22×C32×D3
FittingC23×C3×3−1+2C2
socleC23×C32C2×C32
prime radicalC23×C33C2×C3
cosocleC2×C32C23×C32
hypercenterC23×3−1+2D3
hypocenterC3C22×C4×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×3−1+2

608 conjugacy classes of subgroups; only the 301 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 301 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

264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2596);