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C3×#41×AGL(1,𝔽5) #11756973

order960
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#41×AGL(1,𝔽5)

Splittings

FittingC3×C5×#41 ⋊ C4
HallC3×C5 ⋊ C4×#41
SylowC5 ⋊ C3×C4×#41

Subgroups

subgroupG/H
centerC3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C23×C3×C4
FrattiniC2C23×C3×AGL(1,𝔽5)
FittingC3×C5×#41C4
socleC2×C3×C5C23×C4
prime radicalC3×D5×#41C2
cosocleC2×D5C24×C3
hypercenterC3×#41AGL(1,𝔽5)
hypocenterC5C3×C4×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C3×#41

620 conjugacy classes of subgroups.

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)×#104, AGL(1,𝔽5)×#837, C3×#10604002, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#104, AGL(1,𝔽5)×#837, C3×#10604002, …
maximal quotient ofC3×AGL(1,𝔽5)×#117, C3×C4×D4×AGL(1,𝔽5), C3×C4×Q8×AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11168);