Finite Group Databasebeta

← Prev (#11709083) Next (#11709085) →

C2×#87574 #11709084

order768
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC2×#87574

Splittings

FittingC2×C3×#585 ⋊ C2
SylowC3 ⋊ C2×H(7,𝔽2)

Subgroups

subgroupG/H
centerC22C25×D3
commutator, cosocleC2×C3C27
FrattiniC2C26×D3
FittingC2×C3×#585C2
socleC22×C3C26
hypercenterC2×#585D3
hypocenterC3C2×H(7,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#585

60570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#11661865, C2×D3×H(7,𝔽2), C2×#11661936, …
maximal normal subgroup ofC2×#11661865, C2×D3×H(7,𝔽2), C2×#11661936, …
maximal quotient of#72271193, #72271210, #72271941

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083465);