Finite Group Databasebeta

C2×#20299015 #28403673

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20299015

Splittings

SylowC113 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C8C22×D113
commutatorC2×C113C23×C8
FrattiniC8C23×D113
FittingC2×#131×C113C2
socleC22×C113C22×C8
prime radicalC2×#41×C113C4
cosocleC8×C113C24
hypercenterC2×#131D113
hypocenterC113C2×#504
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C8 ◁ C2×#131

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17609);