Finite Group Databasebeta

C2×#20299396 #28405319

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

Aliases

direct productC2×#20299396

Splittings

FittingC22×#41×C113 ⋊ C2
SylowC113 ⋊ C2×#575

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC22×#41×C113C2
socleC22×C113C22×D4
hypercenterC22×#41D113
hypocenterC113C2×#575
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

1484 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, 19255);