Finite Group Databasebeta

C22×#11763745 #17978847

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×#11763745
unambiguous semidirect productD17⋊(C2×#376)

Splittings

FittingC22×C42×C17 ⋊ C4
SylowC17 ⋊ C22×#376

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC22×C42×C17C4
socleC24×C17C22×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC22×C42#595
hypocenterC17C22×#376
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42

5150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114091);