Finite Group Databasebeta

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D3×#392109 #72249042

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C216

Aliases

direct productD3×#392109

Splittings

FittingC3×#392109 ⋊ C2
SylowC3 ⋊ C2×#392109

Subgroups

subgroupG/H
centerC23C22×D3×C22⋊C4
commutatorC24×C3C24×C4
FrattiniC25C24×D3
FittingC3×#392109C2
socleC23×C3C23×C22⋊C4
prime radicalC25×D3×D4C2
cosocleC25×C3C25
hypercenter#392109D3
hypocenterC3C2×#392109
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C27 ◁ #392109

822922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#72210600, D3×#72213256, D3×#72210555, …
maximal normal subgroup ofD3×#72210600, D3×#72213256, D3×#72210555, …
maximal quotient ofD3×#72210555
automorphism group of#4697, #5056, #5068

GAP

Past the SmallGroups library coverage — no SmallGroups id.