Finite Group Databasebeta

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C5×D3×#3937 #72260130

order4800
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×D3×#3937

Splittings

FittingC3×C42×C52 ⋊ C22
HallC3×C52 ⋊ C2×#104
SylowC52 ⋊ D3×#104
SylowC3 ⋊ C2×C5×#3937

Subgroups

subgroupG/H
centerC4×C5D3×D20
commutatorC3×C4×C5C22×C4×C5
FrattiniC2×C4C2×C5×D3×D5
FittingC3×C42×C52C22
socleC2×C3×C52C2×C22⋊C4
prime radicalC5×D3×#709C2
cosocleC2×C3×C4×C5C23×C5
hypercenterC42×C5D3×D5
hypocenterC3×C5C2×C5×#104
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C42×C5

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#13100574
maximal normal subgroup ofD3×#13100574

GAP

Past the SmallGroups library coverage — no SmallGroups id.