Finite Group Databasebeta

C2×#20299526 #28406927

order14464
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20299526

Splittings

SylowC113 ⋊ C2×#368

Subgroups

subgroupG/H
centerC22#16813691
commutatorC8×C113C22×C4
FrattiniC8C22×#90673
FittingC2×C16×C113C4
socleC22×C113#107
prime radicalC22×D113Q16
cosocleC8×D113C23
hypercenterC2×C16#90673
hypocenterC113C2×#368
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

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, 20863);