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D3×#1913 #10797194

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×#1913

Splittings

FittingC3×#1913 ⋊ C2
SylowC3 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC2D3×#386
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1913C2
socleC2×C3C2×#386
prime radicalD3×#534C2
cosocleC24×C3C24
hypercenter#1913D3
hypocenterC3C2×#1913
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C24 ◁ #1913

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12753, D3×#23895, D3×#23996, …
maximal normal subgroup ofD3×#12753, D3×#23895, D3×#23996, …
maximal quotient ofD3×#9495, D3×#10972, C2×D3×#1913, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 171575);