Finite Group Databasebeta

C4×#16811565 #28312728

order13568
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×#16811565

Splittings

FittingC22×C42×C53 ⋊ C4
SylowC53 ⋊ C4×#380

Subgroups

subgroupG/H
centerC22×C4C22×#6157
commutatorC22×C53C22×C42
FrattiniC23C23×#6157
FittingC22×C42×C53C4
socleC23×C53C23×C4
prime radicalC24×D53C23
cosocleC23×D53C24
hypercenterC22×C42#6157
hypocenterC53C4×#380
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C42

2782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1098204);