Finite Group Databasebeta

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C3×#13088417 #72269765

order4320
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#13088417

Splittings

HallC33×C5 ⋊ C4×D4
SylowC33 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ C3×#63881

Subgroups

subgroupG/H
center, hypercenterC2×C3D32×AGL(1,𝔽5)
commutatorC2×C32×C5C22×C3×C4
FrattiniC2C3×D32×AGL(1,𝔽5)
Fitting, socleC2×C33×C5C22×C4
prime radicalC3×D5×#626C2
cosocleC2×C32×D5C23×C3
hypocenterC32×C5C3×C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2×C3

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#3811
maximal normal subgroup ofC3×AGL(1,𝔽5)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.