Finite Group Databasebeta

← Prev (#72344040) Next (#72344042) →

C2×#72220618 #72344041

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

Aliases

direct productC2×#72220618

Splittings

FittingC2×#36614 ⋊ D3

Subgroups

subgroupG/H
centerC22C22×#1020⋊C2
commutator, cosocleC2×C22⋊A4C25
FrattiniC23C24×S4
FittingC2×#36614D3
socleC24C23×S4
hypercenterC22×C4#1020⋊C2
hypocenterC22⋊A4C2×H(5,𝔽2)
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C22 ◁ C22×C4

36178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72220683
maximal normal subgroup ofC2×#72220683
maximal quotient ofC2×#72246847

GAP

Past the SmallGroups library coverage — no SmallGroups id.