Finite Group Databasebeta

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C2×#72258616 #72258779

order3072
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#72258616

Splittings

FittingC23×H(3,𝔽4) ⋊ D3

Subgroups

subgroupG/H
centerC22#11713964
commutator, cosocleC2×D4×A4C24
FrattiniC2×D4C23×S4
FittingC23×H(3,𝔽4)D3
socleC24#5244
hypercenterC2×H(3,𝔽4)S4
hypocenterA4C2×#2199
LCSG ▷ C2×D4×A4 ▷ C22×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×H(3,𝔽4)

14889 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72258621

GAP

Past the SmallGroups library coverage — no SmallGroups id.