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#11860487

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3

Aliases

No aliases for this group.

Splittings

FittingC32×AGL(1,ℤ/8) ⋊ C4
SylowC32 ⋊ #2946

Subgroups

subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC32×AGL(1,ℤ/8)C4
socleC2×C32C2×C4×D4
prime radicalC3⋊D3×AGL(1,ℤ/8)C2
cosocleC4×C3⋊D3C24
hypercenterAGL(1,ℤ/8)#157
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Polycyclic presentation:

2^7,3^2|a^2=f,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^2i^2,i^a=h^2i,e^b=eg,d^c=dg,h^c=hi,i^c=hi^2,h^f=h^2,i^f=i^2

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94498);