Finite Group Databasebeta

C22×#11763675 #17968148

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11763675

Splittings

SylowC17 ⋊ C22×#336

Subgroups

subgroupG/H
centerC25C2×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC24×C4×C17C4
socle, prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC24×C4#595
hypocenterC17C22×#336
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×C4

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 1103392);