Finite Group Databasebeta

C4×D11×C22⋊Q8 #14912215

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×D11×C22⋊Q8

Splittings

FittingC4×C11×C22⋊Q8 ⋊ C2
SylowC11 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11C2×C4×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328010);