Finite Group Databasebeta

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C2×#72220637 #72241376

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC2×#72220637

Splittings

FittingC2×#36614 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C2×#1020⋊C2
commutator, cosocleC2×C22⋊A4C25
FrattiniC23C24×S4
FittingC2×#36614D3
socleC24C23×S4
hypercenterC22×C4#1020⋊C2
hypocenterC22⋊A4C22×#41
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2×C4 ◁ C22×C4

At least 7562 conjugacy classes of subgroups; only the 544 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72233475, C2×#72258027, C2×#72342683, …
maximal normal subgroup ofC2×#72258027, C2×#72342683, C2×#72220683
maximal quotient ofC2×#72246879
automorphism group ofC2×#504

GAP

Past the SmallGroups library coverage — no SmallGroups id.