Finite Group Databasebeta

C4×D4⋊(C11⋊C8) #14644365

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×D4⋊(C11⋊C8)

Splittings

SylowC11 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D11
commutatorC4×C11C2×C4×C8
FrattiniC2×C42C22×D11
FittingC42×D4×C11C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC42×D4D11
hypocenterC11C4×D4⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 60160);