Finite Group Databasebeta

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D3×#394058 #72247174

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C214

Aliases

direct productD3×#394058

Splittings

FittingC3×#394058 ⋊ C2
SylowC3 ⋊ C2×#394058

Subgroups

subgroupG/H
centerC23C2×D3×#120
commutator, cosocleC25×C3C25
FrattiniC25C24×D3
FittingC3×#394058C2
socleC23×C3C22×#120
hypercenter#394058D3
hypocenterC3C2×#394058
LCSG ▷ C25×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ #394058

At least 8860 conjugacy classes of subgroups; only the 2079 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72210600, D3×#72219157
maximal normal subgroup ofD3×#72210600, D3×#72219157
maximal quotient ofD3×#72210600, D3×#72214549
automorphism group of#4524, C4×D3×C8, C4×ΓL(1,𝔽25), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.