Finite Group Databasebeta

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C2×#72220492 #72344058

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productC2×#72220492

Splittings

FittingC26×D4 ⋊ D3

Subgroups

subgroupG/H
centerC22C23×#1020
commutator, cosocleC2×C22⋊A4C25
FrattiniC2C24×#1020
FittingC26×D4D3
socleC26C23×D3
hypercenterC22×D4#1020
hypocenterC22⋊A4C2×H(5,𝔽2)
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C22 ◁ C22×D4

226104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72220683
maximal normal subgroup ofC2×#72220683
maximal quotient ofC2×#72246309

GAP

Past the SmallGroups library coverage — no SmallGroups id.