Finite Group Databasebeta

C2×#20299399 #28405323

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

Aliases

direct productC2×#20299399

Splittings

FittingC22×D8×C113 ⋊ C2
SylowC113 ⋊ C2×#576

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC22×D8×C113C2
socleC22×C113C22×D4
hypercenterC22×D8D113
hypocenterC113C2×#576
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

1612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19259);