Finite Group Databasebeta

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C8×#634⋊C3 #13141442

order1728
isoclinismisoclinic class of #634⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22×C3

Aliases

direct productC8×#634⋊C3
unambiguous semidirect product(C8×#634)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC4×C8×H(3,𝔽3)C2
socleC22×C3C2×C3×C4×D3
prime radicalC22×H(3,𝔽3)C22×C4
cosocleC2×C32×C4C23×C3
hypercenterC4×C8(C3⋊D3)⋊C3
hypocenterC32C3×C8×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7505);