Finite Group Databasebeta

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#117×(C3⋊D3)⋊C3 #13152514

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C3×C4

Aliases

direct product#117×(C3⋊D3)⋊C3
unambiguous semidirect product(C3⋊D3×#117)⋊C3

Splittings

FittingH(3,𝔽3)×#117 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#117

Subgroups

subgroupG/H
centerC2×C4C22×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#117C2
prime radicalC23×(C3⋊D3)⋊C3C22
cosocleC22×C32C24×C3
hypercenter#117(C3⋊D3)⋊C3
hypocenterC32C2×C3×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

1231 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18577);