Finite Group Databasebeta

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C3×#4314⋊C5 #72216787

order2640
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#4314⋊C5

Splittings

FittingC3×C8×C11 ⋊ C2×C5
HallC3×#4314 ⋊ C5
Hall#4314 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ SD16
HallC11⋊C5 ⋊ C3×SD16
HallC3×C11 ⋊ C5×SD16
SylowC11 ⋊ C3×C5×SD16

Subgroups

subgroupG/H
centerC2×C3C4⋊AGL(1,𝔽11)
commutator, cosocleC4×C11C22×C3×C5
FrattiniC4C2×C3×AGL(1,𝔽11)
FittingC3×C8×C11C2×C5
socleC2×C3×C11C5×D4
prime radicalC3×C4⋊AGL(1,𝔽11)C2
hypercenterC3×C8AGL(1,𝔽11)
hypocenterC11C3×C5×SD16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#66964⋊C5, C3×#66961⋊C5, #72216947, …
maximal normal subgroup ofC3×#66964⋊C5, C3×#66961⋊C5, #72216947, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.