Finite Group Databasebeta

C4⋊C8×C11⋊C8 #14644896

order2816
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8

Aliases

direct productC4⋊C8×C11⋊C8

Splittings

SylowC11 ⋊ C8×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D11
commutatorC2×C11C2×C82
FittingC4×C11×C4⋊C8C2
socle, prime radicalC23×C11C2×C42
cosocleC2×C42×C11C23
hypercenterC4×C4⋊C8D11
hypocenterC11C8×C4⋊C8
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 60691);