Finite Group Databasebeta

C2×#20299351 #28404707

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20299351

Splittings

SylowC113 ⋊ C2×#563

Subgroups

subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#123×C113C2
socleC23×C113C24
prime radicalC22×D4×C113C22
hypercenterC2×#123D113
hypocenterC113C2×#563
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#123

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1606 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 18643);