Finite Group Databasebeta

C4×#11763682 #17956615

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11763682

Splittings

FittingC4×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C4×#340

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC4×C17C43
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenterC4×C4⋊C4#595
hypocenterC17C4×#340
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1091859);