Finite Group Databasebeta

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3−1+2×D19⋊C3 #72244835

order3078
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×D19⋊C3

Splittings

FittingC19×3−1+2 ⋊ C2×C3
Hall3−1+2×C19⋊C3 ⋊ C2
HallD19 ⋊ C3×3−1+2
SylowC19 ⋊ C2×C3×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×D19⋊C3
commutator, socle, cosocleC3×C19C2×C33
FittingC19×3−1+2C2×C3
prime radicalC32×D19⋊C3C3
hypercenter3−1+2D19⋊C3
hypocenterC19C2×C3×3−1+2
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ 3−1+2

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 171

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×AGL(1,𝔽19), AGL(1,ℤ/9)×D19⋊C3
maximal normal subgroup of3−1+2×AGL(1,𝔽19), AGL(1,ℤ/9)×D19⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.