Finite Group Databasebeta

C2×#20298713 #28399462

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20298713

Splittings

FittingC2×#131×C113 ⋊ C2
SylowC113 ⋊ C2×#443

Subgroups

subgroupG/H
centerC2×C8C22⋊D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×#131×C113C2
socleC22×C113C4×D4
prime radicalC2×#16813642C2
cosocleC2×C4×C113C24
hypercenterC2×#131D113
hypocenterC113C2×#443
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13398);