Finite Group Databasebeta

C2×#20299543 #28407020

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

Aliases

direct productC2×#20299543
unambiguous semidirect productD113⋊#383

Splittings

FittingC2×C42×C113 ⋊ C4
SylowC113 ⋊ C2×#383

Subgroups

subgroupG/H
centerC23C22×#90673
commutatorC22×C113C23×C4
FrattiniC22C23×#90673
FittingC2×C42×C113C4
socleC23×C113C22×C4
prime radicalC23×D113C23
cosocleC22×D113C24
hypercenterC2×C42#90673
hypocenterC113C2×#383
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C42

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20956);