Finite Group Databasebeta

C2×#20299410 #28405335

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

Aliases

direct productC2×#20299410

Splittings

FittingC2×#131×C113 ⋊ C2
SylowC113 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C22×D452
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC2×#131×C113C2
socleC22×C113C22×D4
hypercenterC2×#131D113
hypocenterC113C2×#577
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19271);