Finite Group Databasebeta

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C3×#67×C11⋊C5 #72246995

order3960
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×#67×C11⋊C5

Splittings

FittingC22×C32×C11 ⋊ C2×C5
HallC3×C11×#67 ⋊ C5
HallC32×C11⋊C5 ⋊ D4
HallC32×C11 ⋊ C5×D4
SylowC11 ⋊ C3×C5×#67
SylowC32 ⋊ D4×C11⋊C5

Subgroups

subgroupG/H
centerC2×C3C2×D3×C11⋊C5
commutator, cosocleC2×C3×C11C22×C3×C5
FrattiniC2C2×C3×D3×C11⋊C5
FittingC22×C32×C11C2×C5
socleC2×C32×C11C22×C5
hypercenterC22×C3D3×C11⋊C5
hypocenterC3×C11C3×C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2×C3 ◁ C22×C3

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×#3811, C3×#67×AGL(1,𝔽11), #72247217
maximal normal subgroup ofC11⋊C5×#3811, C3×#67×AGL(1,𝔽11), #72247217

GAP

Past the SmallGroups library coverage — no SmallGroups id.