Finite Group Databasebeta

C2×#20299131 #28403839

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

Aliases

direct productC2×#20299131

Splittings

FittingC2×#126×C113 ⋊ C2
SylowC113 ⋊ C2×#529

Subgroups

subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#126×C113C2
socleC23×C113C24
prime radicalC2×#16813595C2
hypercenterC2×#126D113
hypocenterC113C2×#529
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#126

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17775);