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C3×C22⋊C4×AGL(1,𝔽5) #11752231

order960
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×C22⋊C4×AGL(1,𝔽5)

Splittings

FittingC3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ C4×C22⋊C4
SylowC5 ⋊ C3×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3C22×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C42
FrattiniC22C22×C3×AGL(1,𝔽5)
FittingC3×C5×C22⋊C4C4
socleC22×C3×C5C22×C4
prime radicalC23×C3×D5C22
cosocleC22×D5C23×C3
hypercenterC3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 120

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#99, AGL(1,𝔽5)×#806, C2×C3×C22⋊C4×AGL(1,𝔽5), …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#99, AGL(1,𝔽5)×#806, C2×C3×C22⋊C4×AGL(1,𝔽5), …
maximal quotient ofC3×AGL(1,𝔽5)×#95, C3×#10604252, C3×#10603800, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6426);