Finite Group Databasebeta

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C2×#72213984 #72258786

order3072
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct productC2×#72213984

Splittings

Fitting, SylowC2×#5020974 ⋊ C3

Subgroups

subgroupG/H
centerC23C2×#560⋊C3
commutator, cosocleC22×C42C24×C3
FrattiniC24C24×A4
FittingC2×#5020974C3
socleC25C23×A4
hypercenterC22×C4#560⋊C3
hypocenterC42C2×C3×#121
LCSG ▷ C22×C42 ▷ C42
UCSC1 ◁ C23 ◁ C22×C4

12970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72214051
maximal normal subgroup ofC2×#72214051

GAP

Past the SmallGroups library coverage — no SmallGroups id.