Finite Group Databasebeta

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#14680424

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ #14288

Subgroups

subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#14288
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Polycyclic presentation:

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

Conjugacy classes & character table

464 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 96219);