Finite Group Databasebeta

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C3×#72213282 #72230890

order9600
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#72213282

Splittings

FittingC2×C3×C52×D4 ⋊ C2×C4
HallC3×C52 ⋊ C4×AGL(1,ℤ/8)
SylowC52 ⋊ C3×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3C2×#11717375
commutatorC4×C52C23×C3×C4
FrattiniC4C22×C3×D5⋊AGL(1,𝔽5)
FittingC2×C3×C52×D4C2×C4
socleC2×C3×C52C2×C4×D4
prime radicalC3×#13106298C2
cosocleC4×C5⋊D5C24×C3
hypercenterC2×C3×D4D5⋊AGL(1,𝔽5)
hypocenterC52C3×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

3044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#72213282
maximal normal subgroup ofD3×#72213282

GAP

Past the SmallGroups library coverage — no SmallGroups id.