Finite Group Databasebeta

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D3×C22⋊C4×#1043 #72260279

order9600
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productD3×C22⋊C4×#1043

Splittings

FittingC3×C52×C22⋊C4 ⋊ C2×C4
HallC3×C52 ⋊ C2×C4×C22⋊C4
SylowC52 ⋊ C4×D3×C22⋊C4
SylowC3 ⋊ C2×C22⋊C4×#1043

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×#1043
commutatorC2×C3×C52C22×C42
FittingC3×C52×C22⋊C4C2×C4
socleC22×C3×C52C23×C4
prime radicalC23×D3×C5⋊D5C22
cosocleC22×C3×C5⋊D5C24
hypercenterC22⋊C4D3×#1043
hypocenterC3×C52C2×C4×C22⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C22⋊C4

10880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.