Finite Group Databasebeta

C2×#20299480 #28406283

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

Aliases

direct productC2×#20299480

Splittings

FittingC22×C8×C113 ⋊ C4
SylowC113 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊#90673
commutatorC22×C113C2×C42
FrattiniC2×C4C22×#90673
FittingC22×C8×C113C4
socleC22×C113#95
prime radicalC23×D113C2×C4
cosocleC2×C4×D113C23
hypercenterC22×C8#90673
hypocenterC113C2×#344
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20219);