Finite Group Databasebeta

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C2×D3×#11717375 #72259444

order9600
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D3×#11717375

Splittings

FittingC23×C3×C52 ⋊ C22×C4
HallC3×C52 ⋊ C22×C4×D4
SylowC52 ⋊ C2×C4×D3×D4
SylowC3 ⋊ C22×#11717375

Subgroups

subgroupG/H
centerC22C2×D3×D5⋊AGL(1,𝔽5)
commutatorC2×C3×C52C24×C4
FrattiniC2C22×D3×D5⋊AGL(1,𝔽5)
FittingC23×C3×C52C22×C4
socleC22×C3×C52C23×C4
prime radicalC2×D3×#87886C2
cosocleC2×C3×C5⋊D5C25
hypercenterC23D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C22×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C23

12836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3⋊D3×#11717375
maximal quotient ofD3×#72213282, C2×C3⋊D3×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.