Finite Group Databasebeta

#137×#3624 #17966620

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

Aliases

direct product#137×#3624

Splittings

SylowC17 ⋊ C8×#137

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C17×#137C4
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C2×C4
cosocleC4×Dic17C24
hypercenterC2×#137#595
hypocenterC17C8×#137
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101864);