Finite Group Databasebeta

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C2×#10596499 #11918775

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

Aliases

direct productC2×#10596499

Splittings

SylowC32 ⋊ C2×#575

Subgroups

subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#575
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

2374 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, 152786);