Finite Group Databasebeta

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C2×#72241384 #72344138

order3072
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C28

Aliases

direct productC2×#72241384

Splittings

Fitting, SylowC2×#6628896 ⋊ C3

Subgroups

subgroupG/H
center, socleC23C22×#120⋊C3
commutator, cosocleC2×H(5,𝔽2)C24×C3
FrattiniC24C24×A4
FittingC2×#6628896C3
hypercenterC22×D4#120⋊C3
hypocenterH(5,𝔽2)C22×C3×D4
LCSG ▷ C2×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C23 ◁ C22×D4

At least 6406 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72246780, C2×#72246533, C2×#72246181
maximal normal subgroup ofC2×#72246780, C2×#72246533, C2×#72246181

GAP

Past the SmallGroups library coverage — no SmallGroups id.