Finite Group Databasebeta

C2×#20298562 #28399010

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20298562

Splittings

SylowC113 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
FittingC24×C4×C113C2
socleC23×C113C22×C4
prime radicalC25×C113C4
cosocleC2×C4×C113C24
hypercenterC24×C4D113
hypocenterC113C2×#407
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12946);