Finite Group Databasebeta

C2×C4×#14268624 #28392905

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#14268624

Splittings

FittingC22×C42×C113 ⋊ C2
SylowC113 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D113
commutatorC2×C113C22×C42
FrattiniC23C23×D113
FittingC22×C42×C113C2
socleC24×C113C23
prime radicalC24×D113C22
cosocleC23×C113C24
hypercenterC22×C42D113
hypocenterC113C2×C4×C22⋊C4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6841);