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#14760671

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC4×C11×AGL(1,ℤ/8) ⋊ C2
SylowC11 ⋊ #21555

Subgroups

subgroupG/H
centerC22C2×#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C2×#121
prime radicalC2×#10622812C2
cosocleC22×C4×C11C24
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#21555
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Polycyclic presentation:

2^8,11|a^2=g,b^2=e,d^2=g,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=dh,i^b=i^10,f^c=fh

Conjugacy classes & character table

278 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 176466);