Finite Group Databasebeta

#41×#63216 #17978674

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct product#41×#63216

Splittings

SylowC17 ⋊ C16×#41

Subgroups

subgroupG/H
centerC42C22×#595
commutatorC2×C17C23×C16
FrattiniC2×C4C23×#595
FittingC4×#41×C17C4
socleC22×C17C23×C8
prime radicalC2×#41×C17C8
cosocleC2×#3622C24
hypercenterC4×#41#595
hypocenterC17C16×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C4×#41

602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113918);