Finite Group Databasebeta

← Prev (#17968174) Next (#17968176) →

C22×#11763679 #17968175

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11763679

Splittings

FittingC22×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C22×#339

Subgroups

subgroupG/H
centerC24C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC22×C4⋊C4×C17C4
socleC24×C17C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C22×#339
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

2830 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, 1103419);