Finite Group Databasebeta

C2×#20298526 #28393801

order14464
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20298526

Splittings

SylowC113 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D113
commutator, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC22×C22⋊C4×C113C2
socleC24×C113C23
prime radicalC25×C113C22
hypercenterC22×C22⋊C4D113
hypocenterC113C2×#397
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

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, 7737);