Finite Group Databasebeta

C2×#13066833 #14674822

order2816
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13066833

Splittings

SylowC11 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22#10622157
commutator, cosocleC11×C32C23
FrattiniC32C22×D11
FittingC2×C11×Q64C2
socle, prime radicalC22×C11D32
hypercenterC2×Q64D11
hypocenterC11C2×Q128
LCSG ▷ C11×C32 ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×Q64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 90617);