Finite Group Databasebeta

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D3×#3109 #11663341

order768
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD3×#3109

Splittings

FittingC3×#3109 ⋊ C2
SylowC3 ⋊ C2×#3109

Subgroups

subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3109C2
socleC22×C3C23×D4
hypercenter#3109D3
hypocenterC3C2×#3109
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#18524, #72219796, D3×#60558, …
maximal normal subgroup ofD3×#18524, D3×#61451, D3×#60558, …
maximal quotient ofD3×#33688, #72219796, D3×#21452, …
automorphism group of#4487, #4488, #4494, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1037722);