Finite Group Databasebeta

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C2×#10596511 #11900803

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#10596511

Splittings

FittingC22×C32×C4 ⋊ D4
SylowC32 ⋊ C2×#532

Subgroups

subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#532
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134814);