Finite Group Databasebeta

C2×#13067719 #14729486

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13067719

Splittings

FittingC2×D4×Q8×C11 ⋊ C2
SylowC11 ⋊ C2×#1627

Subgroups

subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11#120
prime radicalC2×#10622628C2
hypercenterC2×D4×Q8D11
hypocenterC11C2×#1627
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4×Q8

1290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 145281);