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C2×D3×#361 #10948136

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×#361

Splittings

FittingC2×C3×#361 ⋊ C2
SylowC3 ⋊ C22×#361

Subgroups

subgroupG/H
centerC22D3×#102
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC2×C3×#361C2
socleC22×C3C2×#102
prime radicalC22×D3×D8C2
cosocleC2×C3×C8C24
hypercenterC2×#361D3
hypocenterC3C22×#361
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×AGL(1,ℤ/16), D3×#13037, D3×#12956, …
maximal normal subgroup ofC2×D3×AGL(1,ℤ/16), D3×#13037, D3×#12956, …
maximal quotient ofD3×#12736, C2×C3⋊D3×#361, D32×#361, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322517);