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#14801281

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingQ8×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ #25157

Subgroups

subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterQ8×C22⋊C4D11
hypocenterC11#25157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

1100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Polycyclic presentation:

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

Conjugacy classes & character table

302 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 217076);