Finite Group Databasebeta

C2×#20299414 #28405340

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20299414

Splittings

FittingC2×#137×C113 ⋊ C2
SylowC113 ⋊ C2×#578

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
hypercenterC2×#137D113
hypocenterC113C2×#578
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19276);