Finite Group Databasebeta

C2×#13066450 #14643228

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13066450

Splittings

SylowC11 ⋊ C2×#1277

Subgroups

subgroupG/H
centerC23×C4C22⋊D11
commutatorC4×C11C2×C4×C8
FrattiniC2×C42C22×D11
FittingC22×C11×C4⋊C8C2
socle, prime radicalC24×C11C4⋊C4
cosocleC2×C42×C11C23
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#1277
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 59023);