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#14640968

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

Aliases

No aliases for this group.

Splittings

SylowC11 ⋊ #7277

Subgroups

subgroupG/H
centerC2×C4#66885
commutatorC2×C8×C11C42
FrattiniC2×C4×C8C2×D11
FittingC2×C11×C4⋊C16C2
socleC22×C11#340
prime radicalC23×C11#103
cosocleC2×C4×C8×C11C22
hypercenterC2×C4⋊C16D11
hypocenterC11#7277
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Polycyclic presentation:

2^8,11|a^2=d,b^2=e,c^2=fh,d^2=h,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,i^a=i^10,c^b=cg

Conjugacy classes & character table

458 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 56763);