Finite Group Databasebeta

C2×SD16×C11⋊C8 #14723137

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×SD16×C11⋊C8

Splittings

SylowC11 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenterC2×C4×SD16D11
hypocenterC11C2×C8×SD16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 138932);