Finite Group Databasebeta

C2×#13074658 #14920252

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13074658

Splittings

SylowC11 ⋊ C2×#2652

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2652
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

2070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 336047);