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#14909179

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C11×C16 ⋊ C2
SylowC11 ⋊ #33713

Subgroups

subgroupG/H
centerC2×C4C2×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×C16C2
socleC22×C11C22×D8
hypercenterC2×C4×C16D11
hypocenterC11#33713
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Polycyclic presentation:

2^8,11|b^2=eg,c^2=f,d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,i^a=i^10

Conjugacy classes & character table

716 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 324974);