Finite Group Databasebeta

C2×#13067833 #14729447

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13067833

Splittings

SylowC11 ⋊ C2×#1644

Subgroups

subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1644
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 145242);