Finite Group Databasebeta

C2×#20298671 #28399255

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

Aliases

direct productC2×#20298671

Splittings

FittingC2×#97×C113 ⋊ C2
SylowC113 ⋊ C2×#435

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×#97×C113C2
socleC23×C113C22×C4
prime radicalC22×D452C4
cosocleC2×C4×C113C24
hypercenterC2×#97D113
hypocenterC113C2×#435
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×#97

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

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, 13191);