Finite Group Databasebeta

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C2×#72228560 #72344181

order3072
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C29

Aliases

direct productC2×#72228560

Splittings

Fitting, SylowC2×#10586097 ⋊ C3

Subgroups

subgroupG/H
center, socleC23C23×C22⋊A4
commutator, cosocleC2×H(5,𝔽2)C24×C3
FrattiniC22C24×C22⋊A4
FittingC2×#10586097C3
hypercenterC2×#127C22⋊A4
hypocenterH(5,𝔽2)C22×C3×D4
LCSG ▷ C2×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C23 ◁ C2×#127

278741 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 128

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72246309, C2×#72246076, C2×#72246181
maximal normal subgroup ofC2×#72246309, C2×#72246076, C2×#72246181

GAP

Past the SmallGroups library coverage — no SmallGroups id.