Finite Group Databasebeta

Dic11×#368 #14669187

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productDic11×#368

Splittings

SylowC11 ⋊ C4×#368

Subgroups

subgroupG/H
centerC2×C4D8×D11
commutatorC8×C11C2×C42
FrattiniC22×C8C22×D11
FittingC2×C11×#368C2
socleC22×C11C2×#107
prime radicalC23×C11C2×Q16
cosocleC22×C8×C11C23
hypercenterC2×#368D11
hypocenterC11C4×#368
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84982);