Finite Group Databasebeta

← Prev (#15660392) Next (#15660394) →

#15660393

order2816
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

No aliases for this group.

Splittings

FittingC4×C11×2−1+4 ⋊ C2
SylowC11 ⋊ #62653

Subgroups

subgroupG/H
center, FrattiniC22C25×D11
commutatorC2×C11C25×C4
FittingC4×C11×2−1+4C2
socle, cosocleC22×C11C26
prime radicalC2×D11×2−1+4C2
hypercenterC4×2−1+4D11
hypocenterC11#62653
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×2−1+4

10930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Polycyclic presentation:

2^8,11|a^2=h,c^2=g,d^2=g,b^a=bg,f^a=fg,e^b=eg,d^c=dg,i^f=i^10

Conjugacy classes & character table

470 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076188);