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#14675340

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ #13820

Subgroups

subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13820
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Polycyclic presentation:

2^8,11|a^2=g,b^2=h,c^2=fg,d^2=fg,b^a=be,c^a=cf,i^a=i^10,d^b=de

Conjugacy classes & character table

500 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 91135);