Finite Group Databasebeta

C2×#13066724 #14668695

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13066724

Splittings

SylowC11 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#66896
commutatorC8×C11C2×C42
FrattiniC22×C8C22×D11
FittingC22×C11×#107C2
socleC23×C11#102
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC22×#107D11
hypocenterC11C2×#1387
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84490);