Finite Group Databasebeta

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C2×D4×#1020⋊C2 #72245474

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productC2×D4×#1020⋊C2

Splittings

FittingC2×D4×#120 ⋊ D3

Subgroups

subgroupG/H
centerC22C22×#1020⋊C2
commutator, cosocleC2×C22⋊A4C25
FrattiniC23C24×S4
FittingC2×D4×#120D3
socleC24C23×S4
hypercenterC2×D4#1020⋊C2
hypocenterC22⋊A4C23×D4
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C22 ◁ C2×D4

52820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72240903, C4×D4×#1020⋊C2, C22×D4×#1020⋊C2, …
maximal normal subgroup ofC4×D4×#1020⋊C2, C22×D4×#1020⋊C2, C2×#72220683
maximal quotient of#72245616, C2×#72222918, C4×D4×#1020⋊C2, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.