Finite Group Databasebeta

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C2×C3⋊D3×#1580 #72255377

order4608
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210×C3

Aliases

direct productC2×C3⋊D3×#1580

Splittings

FittingC2×C32×#1580 ⋊ C2
SylowC32 ⋊ C22×#1580

Subgroups

subgroupG/H
centerC22×C4C2×D4×C3⋊D3
commutatorC32×C4C24×C8
FrattiniC42C24×C3⋊D3
FittingC2×C32×#1580C2
socleC23×C32C2×C4×D4
prime radicalC22×D8×C3⋊D3C4
cosocleC32×C42C25
hypercenterC2×#1580C3⋊D3
hypocenterC32C22×#1580
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#1580

16236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#12067
maximal normal subgroup ofC2×C3⋊D3×#12067
maximal quotient ofC2×C3⋊D3×#12067

GAP

Past the SmallGroups library coverage — no SmallGroups id.