Finite Group Databasebeta

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D3×#2905 #11658805

order768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#2905

Splittings

FittingC3×#2905 ⋊ C2
SylowC3 ⋊ C2×#2905

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2905C2
prime radicalC24×D3C2×C4
cosocleC2×C3×C4C25
hypercenter#2905D3
hypocenterC3C2×#2905
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2905

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#11073, D3×#60426, D3×#11071, …
maximal normal subgroup ofD3×#11073, D3×#60426, D3×#11071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033186);