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#117×#272 #13153892

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

Aliases

direct product#117×#272

Splittings

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

Subgroups

subgroupG/H
centerC2×C3×C4C22×C3⋊D3
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C23×C3⋊D3
FittingH(3,𝔽3)×#117C2
prime radicalC23×#272C22
cosocleC22×H(3,𝔽3)C24
hypercenterC3×#117C3⋊D3
hypocenterH(3,𝔽3)C2×#117
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

1815 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, 19955);