Finite Group Databasebeta

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D3×#13100574 #72260184

order9600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#13100574

Splittings

FittingC3×C42×C52 ⋊ C23
HallC3×C52 ⋊ C22×#104
SylowC52 ⋊ C2×D3×#104
SylowC3 ⋊ C2×#13100574

Subgroups

subgroupG/H
centerC4D3×#87877
commutatorC3×C4×C52C23×C4
FrattiniC2×C4C2×D3×D52
FittingC3×C42×C52C23
socleC2×C3×C52C22×C22⋊C4
prime radicalD3×#11717471C2
cosocleC2×C3×C4×C52C24
hypercenterC42D3×D52
hypocenterC3×C52C22×#104
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

4420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.