Finite Group Databasebeta

C22×#11763731 #17978412

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11763731

Splittings

SylowC17 ⋊ C22×#364

Subgroups

subgroupG/H
centerC22×C4C4⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC23×C8×C17C4
socleC23×C17C4⋊C8
prime radicalC24×C17M16
cosocleC2×#3622C24
hypercenterC23×C8#595
hypocenterC17C22×#364
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113656);