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D3×#2177 #10948486

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#2177

Splittings

FittingC3×#2177 ⋊ C2
SylowC3 ⋊ C2×#2177

Subgroups

subgroupG/H
centerC22C2×D3×D8
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC3×#2177C2
socleC22×C3C22×D8
prime radicalC2×D3×D16C2
cosocleC2×C3×C8C24
hypercenter#2177D3
hypocenterC3C2×#2177
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12067, C3⋊D3×#2177, D3×#13658, …
maximal normal subgroup ofD3×#12067, D3×#13658, D3×#7390, …
maximal quotient ofC3⋊D3×#2177, D3×#13658, #72222642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322867);