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C2×C4⋊(C3⋊(C9⋊C8)) #13144227

order1728
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C4⋊(C3⋊(C9⋊C8))

Splittings

SylowC3×C9 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×C3⋊D9
commutatorC2×C3×C9C22×C8
FrattiniC2×C3×C4C22×C3⋊D3
FittingC2×C3×C42×C9C2
socle, prime radicalC23×C32C2×Dic3
cosocleC2×C3×C4×C9C23
hypercenterC2×C42C3⋊D9
hypocenterC3×C9C2×C4⋊C8
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22×C4 ◁ C2×C42

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1728

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10290);