Finite Group Databasebeta

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C5×#63694⋊C3 #72247674

order4320
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#63694⋊C3

Subgroups

subgroupG/H
centerC2×C5C2×((C22⋊C9)⋊C2)⋊C3
commutator, cosocleC2×C22⋊C9C22×C3×C5
FrattiniC2×C3C2×C3×C5×S4
FittingC24×C32×C5D3
socleC23×C3×C5C2×C3×D3
hypercenterC22×C5((C22⋊C9)⋊C2)⋊C3
hypocenterC22⋊C9C3×C5×D4
LCSG ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2×C5 ◁ C22×C5

490 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 180

Conjugacy classes & character table

290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×#72213207, D5×#63694⋊C3
maximal normal subgroup ofD5×#63694⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.