Finite Group Databasebeta

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D3×#13104056 #72259690

order9600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#13104056

Splittings

FittingC3×C52×D4 ⋊ C22×C4
HallC3×C52 ⋊ C2×#442
SylowC52 ⋊ D3×#442
SylowC3 ⋊ C2×#13104056

Subgroups

subgroupG/H
centerC2D3×#11717375
commutatorC3×C4×C52C23×C4
FrattiniC4C2×D3×D5⋊AGL(1,𝔽5)
FittingC3×C52×D4C22×C4
socleC2×C3×C52C2×C4×D4
prime radicalD3×#11717044C2
cosocleC3×C4×C5⋊D5C24
hypercenterD4D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×#442
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C4 ◁ D4

3284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213282
maximal normal subgroup ofD3×#72213282

GAP

Past the SmallGroups library coverage — no SmallGroups id.