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C4⋊Q8×(C3⋊D3)⋊C3 #13153320

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3

Aliases

direct productC4⋊Q8×(C3⋊D3)⋊C3
unambiguous semidirect product(C3⋊D3×C4⋊Q8)⋊C3

Splittings

FittingH(3,𝔽3)×C4⋊Q8 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C4⋊Q8C2
prime radicalC22×(C3⋊D3)⋊C3C23
hypercenterC4⋊Q8(C3⋊D3)⋊C3
hypocenterC32C2×C3×C4⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

1083 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19383);