Finite Group Databasebeta

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D3×#11716874 #72260253

order4800
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD3×#11716874

Splittings

FittingC2×C3×C4×C52 ⋊ C2×C4
HallC3×C52 ⋊ C2×#95
SylowC52 ⋊ D3×#95
SylowC3 ⋊ C2×#11716874

Subgroups

subgroupG/H
center, FrattiniC22C2×D3×#1043
commutatorC2×C3×C52C2×C42
FittingC2×C3×C4×C52C2×C4
socleC22×C3×C52C22×C4
prime radicalC22×D3×C5⋊D5C22
cosocleC22×C3×C5⋊D5C23
hypercenterC2×C4D3×#1043
hypocenterC3×C52C2×#95
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C2×C4

2640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C22⋊C4×#1043
maximal normal subgroup ofD3×C22⋊C4×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.