Finite Group Databasebeta

C22×#11763824 #17979561

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763824

Splittings

SylowC17 ⋊ C22×#430

Subgroups

subgroupG/H
centerC23C2×C4⋊#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC22×M16×C17C4
socleC23×C17C2×C4⋊C4
prime radicalC24×D17Q8
cosocleC4×D17C25
hypercenterC22×M16#595
hypocenterC17C22×#430
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

2718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114805);