Finite Group Databasebeta

C2×#20298366 #28390309

order14464
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20298366

Splittings

SylowC113 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23#14268624
commutatorC22×C113C2×C42
FrattiniC22×C4C22×D113
FittingC22×M16×C113C2
socleC23×C113C22⋊C4
prime radicalC24×C113C2×C4
cosocleC22×C4×C113C23
hypercenterC22×M16D113
hypocenterC113C2×#343
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 4245);