Finite Group Databasebeta

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D4×#4177⋊C3 #72259656

order3888
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32

Aliases

direct productD4×#4177⋊C3

Splittings

FittingD4×#6910 ⋊ C2
Sylow#6910 ⋊ C2×D4

Subgroups

subgroupG/H
centerC2C22×#4177⋊C3
commutator, cosocleC2×C3×C9C23×C32
FrattiniC2×C32C22×C32×D3
FittingD4×#6910C2
socleC2×C3C22×C3×(C3⋊D3)⋊C3
hypercenterD4#4177⋊C3
hypocenterC3×C9C2×C32×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ D4

916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×(#4176⋊C2)⋊C3, D4×(#4169⋊C3)⋊C3
maximal normal subgroup ofD4×(#4176⋊C2)⋊C3, D4×(#4169⋊C3)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.