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C2×#11720586 #13144857

order1728
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11720586

Splittings

SylowH(3,𝔽3) ⋊ C2×#104

Subgroups

subgroupG/H
centerC2×C3×C4#638
commutatorC4×H(3,𝔽3)C22×C4
FrattiniC2×C3×C4C22×C3⋊D3
Fitting, prime radicalC2×#41×H(3,𝔽3)C2
socleC22×C3#3757
cosocleC2×C4×H(3,𝔽3)C23
hypercenterC2×C3×#41C3⋊D3
hypocenterH(3,𝔽3)C2×#104
LCSG ▷ C4×H(3,𝔽3) ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

935 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10920);