Finite Group Databasebeta

C4×#11763788 #17968367

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#11763788

Splittings

FittingC22×C42×C17 ⋊ C4
SylowC17 ⋊ C4×#410

Subgroups

subgroupG/H
centerC42C22⋊#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C22
cosocleC23×D17C24
hypercenterC22×C42#595
hypocenterC17C4×#410
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C42 ◁ C22×C42

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103611);