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#14640688

order2816
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC11 ⋊ #7171

Subgroups

subgroupG/H
centerC22×C4D88
commutatorC8×C11C4×C8
FrattiniC2×C4×C8C2×D11
FittingC2×C4×C11×C16C2
socle, prime radicalC23×C11#102
cosocleC2×C4×C8×C11C22
hypercenterC2×C4×C16D11
hypocenterC11#7171
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Polycyclic presentation:

2^8,11|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^a=i^10

Conjugacy classes & character table

728 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 56483);