Finite Group Databasebeta

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C2×#70929 #10948628

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#70929

Splittings

FittingC2×C3×#444 ⋊ C2
SylowC3 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#5014
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC2×C3×#444C2
socleC22×C3#442
prime radicalC2×#5193C2
cosocleC2×C3×C8C24
hypercenterC2×#444D3
hypocenterC3C2×AGL(1,ℤ/16)
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×AGL(1,ℤ/16), #72219836, #72219845, …
maximal normal subgroup ofC2×D3×AGL(1,ℤ/16), #72219836, #72219845, …
maximal quotient of#72219845, C2×#11797953, D3×#70929, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 323009);