Finite Group Databasebeta

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D3×#13107464 #72231144

order9600
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD3×#13107464

Splittings

HallC3×C52 ⋊ C2×C4×M16
SylowC52 ⋊ C4×D3×M16
SylowC3 ⋊ C2×#13107464

Subgroups

subgroupG/H
center, FrattiniC2C2×D3×AGL(1,𝔽5)2
commutator, socleC2×C3×C52C22×C42
FittingC22×C3×C52C2×C42
prime radicalC22×D3×C5⋊D5C2×C4
cosocleC3×#6036C24
hypercenterC22D3×AGL(1,𝔽5)2
hypocenterC3×C52C2×C4×M16
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C22

2860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72231278
maximal quotient of#72231278
holomorph ofC3×#170

GAP

Past the SmallGroups library coverage — no SmallGroups id.