Finite Group Databasebeta

C2×#13070114 #14782816

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

Aliases

direct productC2×#13070114

Splittings

SylowC11 ⋊ C2×#2088

Subgroups

subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊C8C2
socle, prime radicalC24×C11C2×D4
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#2088
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 198611);