Finite Group Databasebeta

C2×#13067781 #14729494

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

Aliases

direct productC2×#13067781

Splittings

SylowC11 ⋊ C2×#1637

Subgroups

subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenterC2×D4×Q8D11
hypocenterC11C2×#1637
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4×Q8

1174 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, 145289);