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#11817847

order1152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

FittingC32×C4⋊C4 ⋊ D4
SylowC32 ⋊ #2479

Subgroups

subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC22×GO+(4,𝔽2)C22
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2479
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Polycyclic presentation:

2^7,3^2|a^2=e,b^2=f,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,i^b=hi^2,h^c=hi,i^c=i^2,h^g=h^2,i^g=i^2

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 51858);