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#11918778

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

Aliases

No aliases for this group.

Splittings

SylowC32 ⋊ C2×#575

Subgroups

subgroupG/H
centerC4C22×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C23×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#575
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

2374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Polycyclic presentation:

2^7,3^2|d^2=g,f^2=g,b^a=bf,c^a=cg,f^a=fg,i^a=hi^2,f^b=fg,h^b=hi,i^b=i^2,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^2

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 152789);