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#137×#272 #13154389

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

Aliases

direct product#137×#272

Splittings

FittingH(3,𝔽3)×#137 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#137

Subgroups

subgroupG/H
center, socleC2×C3C2×D4×C3⋊D3
commutator, cosocleC4×H(3,𝔽3)C24
FrattiniC3×C4C23×C3⋊D3
FittingH(3,𝔽3)×#137C2
prime radical#41×#272C2
hypercenterC3×#137C3⋊D3
hypocenterH(3,𝔽3)C2×#137
LCSG ▷ C4×H(3,𝔽3) ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#137

1419 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 20452);