Finite Group Databasebeta

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C2×D3×#23895 #72254185

order3072
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C216

Aliases

direct productC2×D3×#23895

Splittings

FittingC2×C3×#23895 ⋊ C2
SylowC3 ⋊ C22×#23895

Subgroups

subgroupG/H
centerC22D3×#2403
commutator, cosocleC24×C3C26
FrattiniC24C25×D3
FittingC2×C3×#23895C2
socleC22×C3C2×#2403
hypercenterC2×#23895D3
hypocenterC3C22×#23895
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#23895

At least 7192 conjugacy classes of subgroups; only the 5767 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#511790, D3×#72219160, D3×#72219157
maximal normal subgroup ofC2×D3×#511790, D3×#72219160, D3×#72219157

GAP

Past the SmallGroups library coverage — no SmallGroups id.