Finite Group Databasebeta

#137×#3633 #17982868

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

Aliases

direct product#137×#3633

Splittings

FittingC17×#137 ⋊ C8
SylowC17 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2C2×D4×#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC17×#137C8
socleC2×C17C2×C8×D4
prime radical#41×D17C2×C4
cosocleC4×#595C24
hypercenter#137#3633
hypocenterC17C8×#137
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118112);